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Contents Computational Number Theory ......................................................3 Secret History: The Story of Cryptology ..........................................3 Game-Theoretical Models in Biology ..............................................4 Introduction to Biological Networks................................................4 Near Rings, Fuzzy Ideals, and Graph Theory ..................................5 Quadratic Irrationals: An Introduction to Classical Number Theory ..............................................................................5

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Algebraic Curves in Cryptography ..................................................6 Handbook of Finite Fields ................................................................6 Discrete Structures and Their Interactions ......................................7 Algebraic Number Fields and Their Completions ............................7 Handbook of Graph Drawing and Visualization ..............................8 Handbook of Graph Theory, Second Edition ..................................8 Handbook of Linear Algebra, Second Edition..................................9 Introduction to Modern Cryptography, Second Edition..................9 Discrete Mathematics with Ducks ................................................10 New Directions of Modern Cryptography ....................................10 Combinatorics of Set Partitions ....................................................11

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Handbook of Finite State Based Models and Applications ............11 Combinatorics of Permutations, Second Edition ..........................12 Cryptology: Classical and Modern with Maplets ..........................12 Transcendental Representations with Applications to Solids and Fluids ......................................................................................13 Combinatorial Scientific Computing ............................................13 Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs ........................................................................14 Parallel Graph Algorithms..............................................................14 The Handbook of Graph Algorithms and Applications, Volume 1: Theory and Optimization ............................................14 The Handbook of Graph Algorithms and Applications, Volume II: Applications ..................................................................14

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Computational Number Theory Abhijit Das Indian Institute of Technology, Kharagpur

Developed from the author’s popular graduate-level course, this self-contained text presents a complete treatment of number-theoretic algorithms. Avoiding advanced algebra and requiring no prior experience with number theory or sophisticated algebraic tools, the book covers many computational aspects of number theory and highlights important and interesting engineering applications. It first builds the foundation of computational number theory by covering the arithmetic of integers and polynomials at a very basic level. It then discusses elliptic curves, primality testing, algorithms for integer factorization, computing discrete logarithms, and methods for sparse linear systems. The text also shows how number-theoretic tools are used in cryptography and cryptanalysis. With an emphasis on implementation issues, it uses the freely available number-theory calculator GP/PARI to demonstrate complex arithmetic computations. The text includes numerous examples and exercises throughout and omits lengthy proofs, making the material accessible to students and practitioners. • Explores many important computational issues and recent developments in number theory • Presents an elementary treatment of the material, eliminating the need for an extensive background in mathematics • Uses the GP/PARI number-theory calculator to illustrate complicated algorithms • Describes the application of number theory in public-key cryptography • Contains numerous examples and exercises, with some solutions in an appendix

Selected Contents: Arithmetic of Integers. Arithmetic of Finite Fields. Arithmetic of Polynomials. Arithmetic of Elliptic Curves. Primality Testing. Integer Factorization. Discrete Logarithms. Large Sparse Linear Systems. Public-Key Cryptography. Appendices. Index. Catalog no. K12950, March 2013, 614 pp. ISBN: 978-1-4398-6615-3, $89.95 / £57.99

Secret History The Story of Cryptology Craig P. Bauer York College of Pennsylvania and National Security Agency Center for Cryptologic History (20112012 Scholar-in-Residence), USA

This work 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 includes interesting instances of codes and ciphers in crime, literature, music, and art. • Presents a unique combination of history and mathematics • Describes the interaction between cryptology and other disciplines such as music, art, literature, politics, and crime • Illustrates the current frontier of cryptologic research through many open problems, including unsolved ciphers • Includes a rich list of references in every chapter, making it easy for readers to pursue the material at an even deeper level • Contains more than 200 illustrations that offer an illuminating look at the subject • Provides hundreds of exercises, real historic ciphers to test skills, and other supplementary material on the book’s CRC Press web page

Selected Contents: CLASSICAL CRYPTOLOGY: Ancient Roots. Monalphabetic Substitution Ciphers, or MASCs: Disguises for Messages. Simple Progression to an Unbreakable Cipher. Transposition Ciphers. Shakespeare, Jefferson, and JFK. World War I and Herbert O. Yardley. Matrix Encryption. World War II: The Enigma of Germany. Cryptologic War against Japan. MODERN CRYPTOLOGY: Claude Shannon. National Security Agency. Data Encryption Standard. Birth of Public Key Cryptography. Attacking RSA. Primality Testing and Complexity Theory. Authenticity. Pretty Good Privacy. Stream Ciphers. Suite B All-Stars. Possible Futures. Index. Catalog no. K15955, April 2013, 620 pp. ISBN: 978-1-4665-6186-1, $69.95 / £44.99

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GameTheoretical Models in Biology

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Mark Broom

Alpan Raval

City University, London, UK

Claremont Graduate University, California, USA

Introduction to Biological Networks

Jan Rychtář University of North Carolina at Greensboro, USA

“… coverage is remarkably wide-ranging, from old standards like the Hawk-Dove game to newer applications such as epidemiology. The authors strike an excellent compromise between breadth and depth by limiting the generality of some theoretical treatments, choosing good examples, and using up-to-date references to round out their coverage. … At the research frontier, the trail has many forks; but whichever fork readers decide to explore, this book will leave them admirably well prepared for the way ahead.” —Mike Mesterton-Gibbons, Florida State University

“… a valuable addition to the bookshelf of anyone working in, or wishing to work in, the area of application of game theoretical approaches to modelling biological phenomena. … this book should become the standard reference for this area. I shall certainly find it an invaluable resource and recommend it highly.” —Chris Cannings, Professor Emeritus, University of Sheffield

• Focuses on the static aspects of game theory and various biological applications • Explores classical evolutionary games as well as a range of modern methods • Presents mathematical models of real and important biological behaviors • Provides source code for the MATLAB® scripts and simulations on the book’s CRC Press web page

Selected Contents: Introduction. What Is a Game? Two Approaches to Game Analysis. Some Classical Games. The Underlying Biology. Matrix Games. Nonlinear Games. Asymmetric Games. Multi-Player Games. Extensive Form Games and Other Concepts in Game Theory. State-Based Games. Games in Finite and Structured Populations. Adaptive Dynamics. The Evolution of Cooperation. Group Living. Mating Games. Food Competition. Predator-Prey and HostParasite Interactions. Epidemic Models. Conclusions. Appendix. Bibliography. Index. Catalog no. K12455, April 2013, 520 pp. ISBN: 978-1-4398-5321-4, $79.95 / £39.99

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Animesh Ray “Raval and Ray provide a comprehensive and modern exposition of a rapidly evolving field: network biology. This text will help biology, mathematics, and computer science students alike to become acquainted with the history and frontiers of research in this exciting area.” —Joshua B. Plotkin, University of Pennsylvania

“Finally a book has arrived that describes the basics of biological complexity. Written by leading scientists Raval and Ray, it provides a scholarly account of the concepts of network theory. It describes in great detail the experimental and computational methods for identifying and predicting biological networks and reveals how network analysis can be applied to solve fundamental questions in biology and medicine. Introduction to Biological Networks is easily the best read available on this important and rapidly developing field.” —Cornelis Murre, University of California-San Diego

The new research area of genomics-inspired network biology lacks an introductory book that enables both physical/computational scientists and biologists to obtain a general yet sufficiently rigorous perspective of current thinking. Filling this gap, this book is the first to offer a broad treatment of genomics-inspired network biology with sufficient mathematical and biological rigor. • Provides a conceptual overview of biological interaction networks as a unifying theme in genomics-inspired biology • Explains the biological significance of interaction networks through numerous examples • Gives a technical introduction to network analysis and the methods by which interaction networks are constructed • Describes relevant biological and mathematical/ statistical concepts in separate boxes • Leads readers from very fundamental concepts to the most current research in biology and medicine

Selected Contents: Introduction. Inferring Networks from Data. Testing Inferred Networks. Small Model Networks. Tractable Network Models. Discussion and Synthesis. Catalog no. C4630, May 2013, 328 pp. ISBN: 978-1-58488-463-7, $79.95 / £49.99 Also available as an eBook

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Near Rings, Fuzzy Ideals, and Graph Theory Bhavanari Satyanarayana Acharya Nagarjuna University, Andra Pradesh, India

Kuncham Syam Prasad Manipal University, India

This reference covers various topics pertaining to near rings with applications and interpretations to fuzzy algebra and graph theory. The authors present the basic notations, simple descriptions, and appropriate illustrations of near rings, fuzzy algebra, and graph theory. They also discuss fundamental decomposition theorems of near rings as well as interesting applications of ideals of near rings to graph theory. The text includes an abundant supply of equations, tables, figures, and photographs to clarify concepts and aid comprehension. • Serves as a functional tool for many interdisciplinary areas • Provides simple, self-explanatory yet comprehensive information • Includes detailed proofs, problems, and examples

Contents: Near Rings: Preliminaries on Set Theory, Groups, and Rings. Near Rings Definitions and Examples. NGroups. Homomorphisms. Ideals of Near Rings: Ideals, Illustrations. Algebra of Ideals, Direct Sums, and Product. Chain Conditions on Ideals. IFP Ideals. Prime Ideals in Near Rings: Prime Ideals. Different Prime Ideals. Characterization of Prime Ideals. Prime Radical. Semiprime Ideals. Nil and Nilpotent Ideals. Dimension and Decompositions in Near Rings: Uniform and Essential Ideals. Finite Goldie Dimension. Dimension Conditions. Some Equivalent Conditions. Primary and Tertiary Decompositions. Gamma Near Rings: Definitions and Examples. Ideals of Gamma Near Rings. Prime Ideals, Nilpotent Ideals of Gamma Near Rings. Modules over Gamma Near Rings (Mr-Groups). Fuzzyness in Near Rings and Gamma Near Rings: Fuzzy Sets and Examples. Fuzzy Ideals of Near Rings and Other Related Algebras. Fuzzy Prime Ideals. Fuzzy Prime Ideals of Gamma Near Rings. Fuzzy Ideals of Mr-Groups. Near Rings and Graphs: Introduction to Graphs. Types of Graphs, Algebra of Graphs. Prime Graph and Graph of Near Ring. Miscellaneous.

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Quadratic Irrationals An Introduction to Classical Number Theory Franz Halter-Koch University of Graz, Austria

This work focuses on the number theory of quadratic irrationalities in various forms, including continued fractions, orders in quadratic number fields, and binary quadratic forms. It presents classical results obtained by the famous number theorists Gauss, Legendre, Lagrange, and Dirichlet. Collecting information previously scattered in the literature, the book covers the classical theory of continued fractions, quadratic orders, binary quadratic forms, and class groups based on the concept of a quadratic irrational. • Presents special results on binary quadratic Diophantine equations and continued fractions, explicit biquadratic class group characters, the divisibility of class numbers by 16, F. Merten’s proof of the Gauss duplication theory, and a theory of binary quadratic forms that departs from the restriction of fundamental discriminants • Brings together the classical theory of continued fractions, quadratic orders, binary quadratic forms, and class groups in a unified way based on the concept of a quadratic irrational • Covers Dirichlet’s theorem on primes in arithmetic progressions and Dirichlet’s class number formula • Reviews the abstract algebra needed to understand the material • Includes many problems and examples suitable for graduate-level courses in number theory

Selected Contents: Review of Elementary Algebra and Number Theory. Quadratic Irrationals. Continued Fractions. Quadratic Residues and Gauss Sums. L-Series and Dirichlet’s Prime Number Theorem. Quadratic Orders. Binary Quadratic Forms. Cubic and Biquadratic Residues. Class Groups. Bibliography. Index. Catalog no. K20533, June 2013, c. 424 pp. ISBN: 978-1-4665-9183-7, $99.95 / £63.99 Also available as an eBook

Catalog no. K13386, June 2013, c. 480 pp. ISBN: 978-1-4398-7310-6, $99.95 / £63.99 Also available as an eBook

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Algebraic Curves in Cryptography

Handbook of Finite Fields

San Ling, Huaxiong Wang, and Chaoping Xing

The Pennsylvania State University, University Park, USA

Gary L. Mullen Daniel Panario

Nanyang Technological University, Singapore

Carleton University, Ottawa, Ontario, Canada

This book systematically addresses the many applications of algebraic geometry to cryptography and coding theory. It provides an introduction to important concepts and demonstrates how to facilitate the new and fruitful connections between the two exciting areas of algebraic geometry and cryptography. The authors expound on a wide range of applications, such as secret sharing, authentication codes, key distributions, frameproof codes, signatures, and broadcast encryption. Each chapter illustrates the connections between algebraic geometry and the specified cryptographic topic and demonstrates how algebraic geometry is used.

Finite fields provide an enabling background for important applications in electrical engineering, computer science, physics, and even biology. While new developments have emerged in recent years, many researchers still use old problem-solving methods that often lead to inaccurate results and solutions.

Selected Contents: Introduction to Algebraic Curves. Introduction to Error-Correcting Codes. Elliptic Curves: Maps between Elliptic Curves. The Group E(Fq) and Its Torsion Subgroups. Computational Considerations on Elliptic Curves. Pairings on an Elliptic Curve. Elliptic Curve Cryptography. Secret Sharing Schemes: The Shamir Threshold Scheme. Other Threshold Schemes. General Secret Sharing Schemes. Information Rate. Quasi-Perfect Secret Sharing Schemes. Linear Secret Sharing Schemes. … Authentication Codes: Authentication Codes. Bounds for A-Codes. A-Codes and Error-Correcting Codes. Universal Hash Families and A-Codes. … Frameproof Codes: Construction without Algebraic Geometry. Asymptotic Bounds and Constructions from Algebraic Geometry. Improvements to the Asymptotic Bound. Key Distribution Schemes: Key Predistribution. Key Predistribution Schemes with Optimal Information Rates. Linear Key Predistribution Schemes. … Broadcast Encryption and Multicast Security: One-Time Broadcast Encryption. Multicast Re-Keying Schemes. Re-Keying Schemes with Dynamic Group Controllers. Some Applications from Algebraic Geometry. Sequences: Linear Feedback Shift Register Sequences. Constructions of Almost Perfect Sequences. … Catalog no. C7946, June 2013, c. 336 pp. ISBN: 978-1-4200-7946-3, $79.95 / £49.99

Poised to become the standard in the field, this stateof-the-art handbook covers all the theoretical aspects of finite fields and presents numerous applications to communications, coding theory, cryptography, elliptic curves, computer science, and physics. The first part of the book spans the history of finite fields through the eighteenth and nineteenth centuries. The second part examines theoretical properties of finite fields while the third part discusses important applications, both mathematical and practical. • Covers nearly all theoretical aspects of the subject • Includes many applications from the fields of computer science and physics • Presents the most important results for each topic without using proofs • Contains over 3,000 references to enable more in-depth study

Selected Contents: INTRODUCTION: History of Finite Fields. Introduction to Finite Fields. THEORETICAL PROPERTIES: Irreducible Polynomials. Primitive Polynomials. Bases. Exponential and Character Sums. Equations over Finite Fields. Permutation Polynomials. Special Functions over Finite Fields. Sequences over Finite Fields. Algorithms. Curves over Finite Fields. Miscellaneous Theoretical Topics. APPLICATIONS: Combinatorial. Algebraic Coding Theory. Cryptography. Miscellaneous Applications. Bibliography. Index. Catalog no. K13417, June 2013, c. 1052 pp. ISBN: 978-1-4398-7378-6, $139.95 / £89.00 Also available as an eBook

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Discrete Structures and Their Interactions

Algebraic Number Fields and Their Completions

Jason I. Brown

Nancy Childress

Dalhousie University, Halifax, Nova Scotia, Canada

Arizona State University, Tempe, USA

This text is intended for graduate and upper-level undergraduate students in mathematics who have taken an initial course in discrete mathematics or graph theory. 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.

This book integrates local and global theory to reflect a very modern view of algebraic number theory. This approach is used whenever possible to make the book as accessible as possible to readers with some background in abstract algebra.

The author explains how the discrete structures have important applications in many areas inside and outside of combinatorics. He also shows how to recognize valuable research connections through these structures.

The author uses contemporary notation and includes numerous examples and end-of-chapter exercises. Suitable for a course on algebraic number theory or as background reading on class field theory, the text covers localization, ramification theory, norms, Minkowski theory, the unit group, cyclotomic fields, and Dedekind domains. • Integrates the treatment of local and global theories

• Emphasizes the connections between different structures and fields

• Serves as a reference for advanced cryptography

• Illustrates how to use discrete structures to represent the salient features and discover the underlying combinatorial principles of seemingly unrelated areas of mathematics and computer science

• Includes exercises and examples

• Contains a variety of exercises that not only highlight the textual material but also encourage students to pursue research-level work

Selected Contents:

• Covers such topics as localization, ramification, norms, and cyclotomic fields

Selected Contents: Algebraic Integers Dedekind Domains Localization Ramification Theory p-adic Numbers

Introduction. Discrete Structures—A Common Framework. Graphs and Directed Graphs. Preorders and Partial Orders. Hypergraphs. Complexes and Multicomplexes. Research Problems. Bibliography. Selected Solutions. Appendices. Index.

Local Fields and Ramification

Catalog no. K16844, July 2013, c. 224 pp. ISBN: 978-1-4665-7941-5, $79.95 / £49.99

The Unit Group

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Abelian Extensions of Q

Norms Different and Discriminant Minkowski Theory Cyclotomic Fields Catalog no. K12415, July 2013, c. 352 pp. ISBN: 978-1-4398-5251-4, $89.95 / £57.99 Also available as an eBook

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Handbook of Graph Drawing and Visualization

Handbook of Graph Theory

Edited by

Roberto Tamassia Brown University, Providence, Rhode Island, USA

This handbook provides a comprehensive survey of the field, from its combinatorial and geometric foundations to its applications in various areas of the physical, life, and social sciences. It offers in-depth coverage of combinatorial, geometric, and algorithmic foundations. With contributions from leading researchers in the field, the book presents numerous graph drawing algorithms as well as graph drawing systems. Applications to mathematics, computer science education, software engineering, database systems, artificial intelligence, telecommunications, bioinformatics, economics, and sociology are also included. • Provides a thorough account of graph drawing and visualization • Presents detailed coverage of combinatorial, geometric, and algorithmic foundations • Includes applications to computer science and bioinformatics

Selected Contents: Combinatorial, Geometric, and Algorithmic Foundations Graph Drawing Algorithms Graph Drawing Systems

Second Edition Edited by

Jonathan L. Gross Columbia University, New York, New York, USA

Jay Yellen Rollins College, Winter Park, Florida, USA

Ping Zhang Western Michigan University, Kalamazoo, USA

Praise for the First Edition: “… a fine guide to various literatures, especially for topics like Ramsey theory … . Many first-rate mathematicians have contributed, making the exposition’s quality high overall. …. Highly recommended.” —CHOICE, January 2005

The most comprehensive single-source guide to graph theory, the new edition of this bestselling handbook covers the most current significant topics in graph theory. Designed with non-experts in mind, this unified, authoritative book makes information easy to find and easy to understand. Each chapter includes lists of definitions and facts accompanied by examples, tables, remarks, a glossary, a bibliography, and, in some areas, conjectures and open problems. • Provides a unified, up-to-date resource on graph theory • Explores the algorithmic and optimization approaches of graph theory as well as “pure” graph theory

Applications

• Unifies the diversity of graph theory terminology and notation

Catalog no. C4126, August 2013, c. 862 pp. ISBN: 978-1-58488-412-5, $99.95 / £63.99

• Bridges theory and practice with many easy-to-read algorithms

Selected Contents: Introduction to Graphs. Graph Representation. Directed Graphs. Connectivity and Traversability. Colorings and Related Topics. Algebraic Graph Theory. Topological Graph Theory. Analytic Graph Theory. Graphical Measurement. Graphs in Computer Science. Networks and Flows. Catalog no. K13767, July 2013, c. 1408 pp. ISBN: 978-1-4398-8018-0, $139.95 / £89.00 Also available as an eBook

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Handbook of Linear Algebra Second Edition Edited by

Leslie Hogben

Introduction to Modern Cryptography Second Edition Jonathan Katz University of Maryland, College Park, USA

Iowa State University, Ames, USA

Yehuda Lindell

Updated and expanded, the second edition of this widely praised bestseller provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use handbook format. It guides readers from the very elementary aspects of the subject to the frontiers of current research. The book encompasses the fundamentals of linear algebra, combinatorial and numerical linear algebra, and applications of linear algebra to various disciplines.

Bar-Ilan University, Ramat Gan, Israel

• Presents both basic and advanced linear algebra concepts, such as matrix perturbation theory and inverse eigenvalue problems • Uses matrix notation throughout the text • Covers combinatorial and numerical linear algebra • Explores mathematical and nonmathematical applications, such as quantum computing, control theory, signal processing, and computational biology • Discusses software packages useful for linear algebra computations, including MATLAB®, Maple™, and Mathematica® • Provides numerous references for additional information along with a glossary that covers all major linear algebra terminology

Selected Contents: Basic Linear Algebra. Matrices with Special Properties. Advanced Linear Algebra. Topics in Advanced Linear Algebra. Matrices and Graphs. Topics in Combinatorial Matrix Theory. Numerical Methods for Linear Systems. Numerical Methods for Eigenvalues. Computational Linear Algebra. Applications to Optimization. Applications to Probability and Statistics. Applications to Analysis. Applications to Physical and Biological Sciences. Applications to Computer Science. Applications to Geometry. Applications to Algebra. Interactive Software for Linear Algebra. Packages of Subroutines for Linear Algebra. Catalog no. K14662, July 2013, c. 1824 pp. ISBN: 978-1-4665-0728-9, $169.95 / £108.00 Also available as an eBook

This updated and expanded second edition of a lauded text provides a rigorous yet accessible account of modern cryptography, focusing on formal definitions, assumptions, and rigorous proofs of security. The first half of the book gives an extensive treatment of private-key cryptography, including encryption, message authentication, and design principles for block ciphers. The second half focuses on public-key cryptography, including number theory; the RSA, DiffieHellman, and El Gamal cryptosystems; public-key encryption and digital signatures; and the random oracle model and its applications. • Includes formal definitions, precise assumptions, and rigorous proofs • Assumes minimal prerequisites, with all necessary mathematical background included in the text • Discusses many widely used cryptographic algorithms and standards • Covers pseudorandom generators/functions, Paillier encryption, and the random oracle model—topics not often found in other texts • Contains suggestions for further reading as well as numerous exercises at the end of each chapter

Selected Contents: Introduction. Perfectly Secret Encryption. Private-Key Encryption and Pseudorandomness. Message Authentication Codes and Collision-Resistant Hash Functions. Practical Constructions of Pseudorandom Permutations (Block Ciphers). Theoretical Constructions of Pseudorandom Objects. Number Theory and Cryptographic Hardness Assumptions. Factoring and Computing Discrete Logarithms. Private-Key Management and the Public-Key Revolution. Public-Key Encryption. Additional PublicKey Encryption Schemes. Digital Signature Schemes. Public-Key Cryptosystems in the Random Oracle Model. Appendices. Index. Catalog no. K16475, September 2013, 640 pp. ISBN: 978-1-4665-7026-9, $79.95 / £40.99 Also available as an eBook

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Discrete Mathematics with Ducks sarah-marie belcastro

New Directions of Modern Cryptography

Research Associate, Smith College, Northampton, Massachusetts, USA

Zhenfu Cao Shanghai Jiao Tong University, China

“When I used Discrete Mathematics with Ducks in class, I assigned readings and my students came to class full of questions and ideas. … these classes were a highlight of my teaching career. I give a lot of credit to this book, thanks to the author’s skill at blending rigor, great examples, casual humor, and precise writing.”

This volume presents the fundamental definitions, precise assumptions, and rigorous security proofs of cryptographic primitives and related protocols. It also describes how they originated from security requirements and how they are applied. The author provides vivid demonstrations of how modern cryptographic techniques can be used to solve security problems. The applications cover wired and wireless communication networks, satellite communication networks, multicast/broadcast and TV networks, and newly emerging networks. The book also.

—David Perkins, author of Calculus and Its Origins

“I think the discovery/exploratory/problem-solving approach is ABSOLUTELY the way this course should be taught, and of all the discrete books I have looked at, this text does the best job of supporting that kind of approach to the subject while still giving enough of the material in writing to fill in the gaps. … I found that the material provided and the instructor notes cut down on my prep time, and I definitely referred to them. Having the in-class activities included is a huge benefit to this book.” —Dana Rowland, Merrimack College

“… an incredible book … readable by students, useful for instructors, and constructed with style and flair. This book will make it much easier to teach an exciting, student-centered discrete mathematics course that will also serve as an excellent introduction to advanced critical thinking, problem solving, and proofs.” —Douglas Shaw, University of Northern Iowa

Selected Contents: Basics: Basic Counting. Set Theory and Logic. Graphs. Induction. Algorithms and Ciphers. Combinatorics: Binomial Coefficients and Permutations. Balls and Boxes and PIE. Recurrence. Counting and Geometry. Graph Theory: Trees. Euler’s Formula. Traversals. Coloring. Supplemental/Optional Material: Probability. Cardinality. Catalog no. K14547, June 2012, 580 pp. ISBN: 978-1-4665-0499-8, $59.95 / £39.95 Also available as an eBook

• Introduces the latest modern cryptographies, including proxy re-cryptography, attributebased cryptography, batch cryptography, and noncommutative cryptography • Emphasizes the core idea that cryptography is born and developed for the application requirements • Presents applications of modern cryptographies to show their practical value in everyday life • Addresses some open problems that challenge the new directions of cryptography

Selected Contents: Introduction: Trust Problem. Ciphertext Access Control Problem. Efficiency Problems in MultiMessage Cryptology. The Challenges from Quantum and Biological Computing. Organization. Proxy ReCryptography: Introduction. Proxy Re-Signature. Proxy Re-Encryption. Attribute-Based Cryptography: Universal Definitions. Bounded Ciphertext-Policy Encryption Schemes. MultiAuthority Encryption Schemes. Interval Encryption Schemes. Fuzzy Identity-Based Signature Schemes. Batch Cryptography: Aggregate Signature and Batch Verification. Batch Decryption and Batch Key Agreement. Batch RSA’s Implementation Based on Diophantine Equations. Solving the Diophantine Equations. Noncommutative Cryptography: BraidBased Cryptography. Z-Modular Method. Using Monomials in Z-Modular Method. Improved Key Exchange over Thompson’s Group. Perspectives. Appendices. Catalog no. K14392, December 2012, 400 pp. ISBN: 978-1-4665-0138-6, $99.95 / £63.99 Also available as an eBook

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Combinatorics of Set Partitions Toufik Mansour

Handbook of Finite State Based Models and Applications Edited by

Jiacun Wang

University of Haifa, Israel

Monmouth University, West Long Branch, New Jersey, USA

Focusing on a very active area of mathematical research in the last decade, this book presents methods used in the combinatorics of pattern avoidance and pattern enumeration in set partitions. Each chapter gives historical perspectives, contrasts different approaches, and illustrates methods and definitions with worked examples and Maple™ code. The text also explores research directions and includes end-ofchapter problems that often draw on real-world data. C++ programs and output tables are listed in the appendices and available for download online.

Applicable to any problem that requires a finite number of solutions, finite state based models (also called finite state machines or finite state automata) have found wide use in various areas of computer science and engineering. This handbook provides a complete collection of introductory materials on finite state theories, algorithms, and the latest domain applications. For beginners, the book is a handy reference for quickly looking up model details. For more experienced researchers, it is suitable as a source of in-depth study in this area.

• Provides a self-contained, accessible introduction to historical and current research on enumeration of and pattern avoidance in set partitions

• Provides extensive coverage of theory and building blocks

• Presents several links between set partitions and areas of mathematics and physics • Describes a variety of tools and approaches useful in other topics of enumerative combinatorics • Includes open questions for further research or projects as well as an extensive bibliography

• Includes examples of applications in each chapter • Discusses automata-based programming • Presents advanced applications in areas such as FPGA design, graph-structured data query, security protocol model checking, and XML processing

• Contains end-of-chapter exercises, with hints and solutions in an appendix

• Offers comprehensive algorithms for automata minimization, incremental construction, optimal adaptive pattern matching, and model checking

• Offers C++ programs and their outputs on the author’s web page

Selected Contents:

Selected Contents: Introduction. Basic Tools of the Book. Generating Functions. Preliminary Results on Set Partitions. Subword Statistics on Set Partitions. Nonsubword Statistics on Set Partitions. Avoidance of Patterns in Set Partitions. Multi Restrictions on Set Partitions. Asymptotics and Random Set Partition. Gray Codes, Loopless Algorithms and Set Partitions. Set Partitions and Normal Ordering. Appendices. Bibliography. Index. Catalog no. K12931, July 2012, 516 pp. ISBN: 978-1-4398-6333-6, $99.95 / £63.99 Also available as an eBook

Finite Automata. Large-Scale Regular Expression Matching on FPGA. Finite State Transducers. Tree Automata. Timed Automata. Quantum Finite Automata. Finite Automata Minimization. Incremental Construction of Finite-State Automata. Esterel and the Semantics of Causality. Regular Path Queries on Graph-Structured Data. Applying Timed Automata to Model Checking of Security Protocols. Optimal Adaptive Pattern-Matching Using Finite State Automata. Finite State Automata in Compilers. Finite State Models for XML Processing. Petri Nets. Statecharts. Model Checking. System Modeling with UML State Machines. Index. Catalog no. K12067, October 2012, 409 pp. ISBN: 978-1-4398-4618-6, $99.95 / £63.99 Also available as an eBook

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Cryptology Combinatorics of Permutations Second Edition

Classical and Modern with Maplets Richard E. Klima Appalachian State University, Boone, North Carolina, USA

Miklós Bóna University of Florida, Gainesville, USA

Neil P. Sigmon

“… an excellent book on an important subject.”

“All told, the authors have done an admirable job of balancing the competing goals of producing a text that can be read by people with limited mathematics background, but at the same time is maintained at a college level. This is not ‘cryptology for dummies,’ watered down to the point of uselessness, but is instead a book that, though accessible, requires an appropriate amount of effort and thought on the part of the reader. … This is a book that not only meets but exceeds its goal of being a suitable text for a course in cryptology for non-majors. It is highly recommended for anybody teaching such a course, and it certainly belongs in any good university library.”

—Fernando Q. Gouvêa, MAA Reviews, December 2012 (This book is in the MAA’s basic library list.)

“… a comprehensive, engaging, and eminently readable introduction to all aspects of the combinatorics of permutations. The chapter on pattern avoidance is especially timely and gives the first systematic treatment of this fascinating and active area of research. This book can be utilized at a variety of levels, from random samplings of the treasures therein to a comprehensive attempt to master all the material and solve all the exercises. In whatever direction the reader’s tastes lead, thorough enjoyment and appreciation of a beautiful area of combinatorics are certain to ensue.” —From the Foreword by Richard Stanley, MIT

A 2006 CHOICE Outstanding Academic Title, the first edition of this bestseller was lauded for its detailed yet engaging treatment of permutations. With much of the book significantly revised and expanded, this second edition includes new material on alternating permutations, multivariate applications, pattern avoidance, and asymptotically normal distributions. It also contains a new chapter on three sorting algorithms from molecular biology.

Selected Contents: In One Line and Close. Permutations as Linear Orders. In One Line and Anywhere. Permutations as Linear Orders. Inversions. In Many Circles. Permutations as Products of Cycles. In Any Way but This. Pattern Avoidance. The Basics. In This Way but Nicely. Pattern Avoidance. Follow-Up. Mean and Insensitive. Random Permutations. Permutations versus Everything Else. Algebraic Combinatorics of Permutations. Get Them All. Algorithms and Permutations. How Did We Get Here? Permutations as Genome Rearrangements. Solutions to OddNumbered Exercises. References. List of Frequently Used Notation. Index.

Radford University, Virginia, USA

—Mark Hunacek, MAA Reviews, September 2012

In a clear, nontechnical manner, this text explains how fundamental mathematical concepts are the bases of cryptographic algorithms. It covers the Enigma machine and Navajo code used during World War II, describes the implementation and cryptanalysis of classical ciphers, and gives straightforward explanations of the AES, public-key ciphers, and message authentication. The book assumes minimal mathematical prerequisites and incorporates easy-to-use Maplets throughout that provide practical examples of the techniques. The Maplets are available for download online.

Selected Contents: Introduction to Cryptology. Substitution Ciphers. Transposition Ciphers. The Enigma Machine and Navajo Code. Shift and Affine Ciphers. Alberti and Vigenère Ciphers. Hill Ciphers. RSA Ciphers. ElGamal Ciphers. The Advanced Encryption Standard. Message Authentication. Bibliography. Hints or Answers to Selected Exercises. Index. Catalog no. K13332, June 2012, 548 pp. ISBN: 978-1-4398-7241-3, $79.95 / £49.99 Also available as an eBook

Catalog no. K12299, June 2012, 478 pp. ISBN: 978-1-4398-5051-0, $89.95 / £57.99 Also available as an eBook

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Transcendental Representations with Applications to Solids and Fluids

Combinatorial Scientific Computing Edited by

Uwe Naumann

L.M.B.C. Campos

RWTH Aachen University, Germany

Lisbon Technical University, Portugal

Olaf Schenk University of Lugano, Switzerland

Building on the author’s previous book Complex Analysis with Applications to Flows and Fields, this work focuses on four infinite representations: series expansions, series of fractions for meromorphic functions, infinite products for functions with infinitely many zeros, and continued fractions as alternative representations. The book also continues the application of complex functions to more classes of fields, including incompressible rotational flows, compressible irrotational flows, unsteady flows, rotating flows, surface tension and capillarity, deflection of membranes under load, torsion of rods by torques, plane elasticity, and plane viscous flows.

This volume explores the latest research on creating algorithms and software tools to solve key combinatorial problems on large-scale high-performance computing architectures. It focuses on load balancing and parallelization, large-scale optimization, algorithmic differentiation of numerical simulation code, sparse matrix software tools, and combinatorial challenges and applications in large-scale social networks. The authors unify these seemingly disparate areas through a common set of abstractions and algorithms.

• Provides mathematical models of physical phenomena and engineering processes particularly relevant in aerospace and mechanical engineering

• Covers a range of topics in scientific computing, including scalable algorithms, software, architectures, and application development

• Unifies interdisciplinary topics of physics, mathematics, and engineering • Explores the interplay between physical laws and mathematical methods as a basis for modeling natural phenomena and engineering devices • Includes examples of applications with interpretation of results and discussion of assumptions and their consequences • Enables readers to construct mathematicalphysical models suited to new observations or novel engineering devices • Contains many illustrations, tables, and diagrams that clarify the links between topics

Selected Contents: Sequences of Fractions or Products. Compressible and Rotational Flows. Exponential and Logarithmic Functions. Plane Elasticity and Multiharmonic Functions. Circular and Hyperbolic Functions. Membranes, Capillarity, and Torsion. Infinite and Cyclometric Representations. Confined and Unsteady Flows. Infinite Processes and Summability. Twenty Examples. Bibliography. Index. Catalog no. K11546, April 2012, 898 pp. ISBN: 978-1-4398-3431-2, $149.95 / £89.00 Also available as an eBook

• Provides an overview of modern combinatorial graph algorithms in computational science

• Focuses on discrete data structures in computational science, such as hypergraph partitioning, vertex and edge reordering and coloring, and bipartite graph matching • Presents applications of high-performance scientific computing in biomedicine, fluid dynamics, and social science

Selected Contents: Combinatorial Scientific Computing: Past Successes, Current Opportunities, Future Challenges. Combinatorial Problems in Solving Linear Systems. Combinatorial Preconditioners. Scalable Hybrid Linear Solvers. Combinatorial Problems in Algorithmic Differentiation. Combinatorial Problems in OpenAD. Getting Started with ADOL-C. Algorithmic Differentiation and Nonlinear Optimization for an Inverse Medium Problem. Combinatorial Aspects/Algorithms in Computational Fluid Dynamics. Unstructured Mesh Generation. 3D Delaunay Mesh Generation. Two-Dimensional Approaches to Sparse Matrix Partitioning. Parallel Partitioning, Ordering, and Coloring in Scientific Computing. Scotch and PT-Scotch Graph Partitioning Software: An Overview. … Catalog no. K11349, January 2012, 600 pp. ISBN: 978-1-4398-2735-2, $89.95 / £57.99 Also available as an eBook

For more information and complete contents, visit www.crcpress.com

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Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs Jason J. Molitierno Sacred Heart University, Fairfield, Connecticut, USA

“… this book works well as a reference textbook for undergraduates. Indeed, it is a distillation of a number of key results involving, specifically, the Laplacian matrix associated with a graph (which is sometimes called the ‘nodal admittance matrix’ by electrical engineers). … a well-written source of background on this growing field. The sources are some of the seminal ones in the field, and the book is accessible to undergraduates.” —John T. Saccoman, MAA Reviews, October 2012

Catalog no. K12933, January 2012, 425 pp. ISBN: 978-1-4398-6337-4, $89.95 / £57.99 Also available as an eBook

Coming soon!

The Handbook of Graph Algorithms and Applications Volume I: Theory and Optimization Krishnaiyan Thulasiraman, Tako Nishizeki, and Guoliang Xue Focusing on design, proof of correctness, and complexity analysis, the first volume presents a detailed discussion of algorithms that are useful in a variety of applications and provides an authoritative review of the current state of the art. Using figures to help illustrate the concepts, the book examines topics, such as incremental algorithms and online algorithms, that have yet to receive much attention but have great potential for future applications. Catalog no. C5955, November 2013, 1216 pp. ISBN: 978-1-58488-595-5, $129.95 / £82.00 Also available as an eBook

Volume II: Applications

Coming soon!

Parallel Graph Algorithms Edited by

David A. Bader Georgia Institute of Technology, Atlanta, USA

To efficiently solve large-scale graph problems, it is necessary to design high-performance computing systems and novel parallel algorithms. In this book, some of the world’s most renowned experts explore the latest research and applications in this important area. The book covers benchmarks, programming, architecture, and applications. It presents the theoretical foundations of graph theory and graph algorithms and describes applications in social network analysis, machine learning, biology, map routing, and more.

Krishnaiyan Thulasiraman, Arun Kumar Somani, and Sarma Vrudhula The second volume focuses on a wide range of algorithmic applications, including graph theory problems. It emphasizes new algorithms and approaches that have been triggered by applications. The book requires minimal exposure to related technologies in order to understand the various approaches. Each chapter is devoted to a single application area, from VLSI circuits to optical networks to program graphs, and features an introduction by a pioneering researcher in that particular field. Catalog no. C5971, November 2013, 1024 pp. ISBN: 978-1-58488-597-9, $119.95 / £76.99 Also available as an eBook

Catalog no. K16641, December 2013, c. 400 pp. ISBN: 978-1-4665-7326-0, $89.95 / £57.99 Also available as an eBook

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Call for Authors Encompassing over 60 books, the Discrete Mathematics and Its Applications series edited by Kenneth H. Rosen publishes leading references, handbooks, and textbooks, including Cryptography: Theory and Practice, Third Edition by Douglas R. Stinson and the Handbook of Linear Algebra edited by Leslie Hogben (new edition coming soon). If you have a book proposal for this series, email publisher Sunil Nair at sunil.nair@informa.com. CRC Press/Taylor & Francis 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487, USA

6000 Broken Sound Parkway, NW, Suite 300 Boca Raton, FL 33487, USA

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