Discrete Mathematics and Combinatorics

See what you’re missing.

SIGN UP NOW

for EXCLUSIVE email offers

at www.crcpress.com

http://www.crcpress.com/product/isbn/9781466504998






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

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

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

Page 6 Page 9

DZM02 5.5x8.5 MC_ISSUU 4.18.13bh

e-mail: [email protected] • 1-859-727-5000

+44 (0) 1235 400 524

Join the CRC Press online community!

Sign up for email alerts at CRCPress.comand be the first to know about

new books in your area of interest. You will also be eligible for:

• Exclusive discounts• Content• Event announcements• New book alerts• FREE shipping

only available in our email and print promotions. Take full advantage of yourinsider savings and free shipping when you buy directly from CRCPress.com

http://www.crcpress.com

To view more information and complete tables of contents for

these and many other related books,

Visit us atwww.crcpress.com

Page 9 Page 10

Page 12 Page 12

http://issuu.com/action/page?page=6

















3For more information and complete contents, visit www.crcpress.com

New!

ComputationalNumber TheoryAbhijit DasIndian Institute of Technology,Kharagpur

Developed from the author’s popular graduate-levelcourse, this self-contained text presents a completetreatment of number-theoretic algorithms. Avoidingadvanced algebra and requiring no prior experiencewith number theory or sophisticated algebraic tools,the book covers many computational aspects of num-ber theory and highlights important and interestingengineering applications.

It first builds the foundation of computational numbertheory by covering the arithmetic of integers andpolynomials at a very basic level. It then discusseselliptic curves, primality testing, algorithms for integerfactorization, computing discrete logarithms, andmethods for sparse linear systems. The text also showshow number-theoretic tools are used in cryptographyand cryptanalysis.

With an emphasis on implementation issues, it usesthe freely available number-theory calculator GP/PARIto demonstrate complex arithmetic computations.The text includes numerous examples and exercisesthroughout and omits lengthy proofs, making thematerial accessible to students and practitioners.

• Explores many important computational issuesand recent developments in number theory

• Presents an elementary treatment of the material, eliminating the need for an extensivebackground in mathematics

• Uses the GP/PARI number-theory calculator toillustrate complicated algorithms

• Describes the application of number theory inpublic-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 EllipticCurves. 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 / £57.99Also available as an eBook

New!

Secret HistoryThe Story ofCryptologyCraig P. BauerYork College of Pennsylvania andNational Security Agency Centerfor Cryptologic History (2011-2012 Scholar-in-Residence), USA

This work gives a thorough yet accessible treatment of both the mathematics and history of cryptology.Requiring minimal mathematical prerequisites, thebook presents the mathematics in sufficient detail andweaves the history throughout the chapters. In addi-tion to the fascinating historical and political sides ofcryptology, the author includes interesting instancesof codes and ciphers in crime, literature, music, andart.

• Presents a unique combination of history andmathematics

• Describes the interaction between cryptologyand other disciplines such as music, art, literature, politics, and crime

• Illustrates the current frontier of cryptologicresearch 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 offeran illuminating look at the subject

• Provides hundreds of exercises, real historicciphers to test skills, and other supplementarymaterial 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 anUnbreakable Cipher. Transposition Ciphers.Shakespeare, Jefferson, and JFK. World War I andHerbert O. Yardley. Matrix Encryption. World War II:The Enigma of Germany. Cryptologic War againstJapan. 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



4 Save when you order online at www.crcpress.com

New!

Game-TheoreticalModels inBiologyMark BroomCity University, London, UK

Jan RychtářUniversity of North Carolina atGreensboro, USA

“… coverage is remarkably wide-ranging, from oldstandards like the Hawk-Dove game to newer appli-cations such as epidemiology. The authors strike anexcellent compromise between breadth and depth bylimiting the generality of some theoretical treatments,choosing good examples, and using up-to-date refer-ences to round out their coverage. … At the researchfrontier, the trail has many forks; but whichever forkreaders decide to explore, this book will leave themadmirably well prepared for the way ahead.”

—Mike Mesterton-Gibbons, Florida State University

“… a valuable addition to the bookshelf of anyoneworking in, or wishing to work in, the area of appli-cation of game theoretical approaches to modellingbiological phenomena. … this book should becomethe standard reference for this area. I shall certainlyfind it an invaluable resource and recommend ithighly.”

—Chris Cannings, Professor Emeritus, University of Sheffield

• Focuses on the static aspects of game theoryand various biological applications

• Explores classical evolutionary games as well as a range of modern methods

• Presents mathematical models of real andimportant biological behaviors

• Provides source code for the MATLAB® scriptsand simulations on the book’s CRC Press webpage

Selected Contents:

Introduction. What Is a Game? Two Approaches toGame Analysis. Some Classical Games. TheUnderlying Biology. Matrix Games. NonlinearGames. Asymmetric Games. Multi-Player Games.Extensive Form Games and Other Concepts in GameTheory. State-Based Games. Games in Finite andStructured Populations. Adaptive Dynamics. TheEvolution of Cooperation. Group Living. MatingGames. Food Competition. Predator-Prey and Host-Parasite Interactions. Epidemic Models. Conclusions.Appendix. Bibliography. Index.

Catalog no. K12455, April 2013, 520 pp.ISBN: 978-1-4398-5321-4, $79.95 / £39.99

Coming soon!

Introduction toBiologicalNetworksAlpan RavalClaremont Graduate University,California, USA

Animesh Ray“Raval and Ray provide a comprehensive and mod-ern exposition of a rapidly evolving field: networkbiology. This text will help biology, mathematics,and computer science students alike to becomeacquainted with the history and frontiers of researchin this exciting area.”

—Joshua B. Plotkin, University of Pennsylvania

“Finally a book has arrived that describes the basicsof biological complexity. Written by leading scien-tists Raval and Ray, it provides a scholarly accountof the concepts of network theory. It describes ingreat detail the experimental and computationalmethods for identifying and predicting biologicalnetworks and reveals how network analysis can beapplied to solve fundamental questions in biologyand medicine. Introduction to BiologicalNetworks is easily the best read available on thisimportant and rapidly developing field.”

—Cornelis Murre, University of California-San Diego

The new research area of genomics-inspired networkbiology lacks an introductory book that enables bothphysical/computational scientists and biologists toobtain a general yet sufficiently rigorous perspectiveof current thinking. Filling this gap, this book is thefirst to offer a broad treatment of genomics-inspirednetwork biology with sufficient mathematical and biological rigor.

• Provides a conceptual overview of biologicalinteraction networks as a unifying theme ingenomics-inspired biology

• Explains the biological significance of interactionnetworks through numerous examples

• Gives a technical introduction to network analysis and the methods by which interactionnetworks are constructed

• Describes relevant biological and mathematical/statistical concepts in separate boxes

• Leads readers from very fundamental concepts tothe most current research in biology and medicine

Selected Contents:

Introduction. Inferring Networks from Data. TestingInferred Networks. Small Model Networks. TractableNetwork Models. Discussion and Synthesis.

Catalog no. C4630, May 2013, 328 pp.ISBN: 978-1-58488-463-7, $79.95 / £49.99Also available as an eBook




Coming soon!

Near Rings,Fuzzy Ideals,and GraphTheoryBhavanariSatyanarayanaAcharya Nagarjuna University,Andra Pradesh, India

Kuncham Syam PrasadManipal University, India

This reference covers various topics pertaining to nearrings with applications and interpretations to fuzzyalgebra and graph theory. The authors present thebasic notations, simple descriptions, and appropriateillustrations of near rings, fuzzy algebra, and graphtheory. They also discuss fundamental decompositiontheorems of near rings as well as interesting applica-tions of ideals of near rings to graph theory. The textincludes an abundant supply of equations, tables, fig-ures, and photographs to clarify concepts and aidcomprehension.

• 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. N-Groups. Homomorphisms.Ideals of Near Rings: Ideals, Illustrations. Algebra ofIdeals, Direct Sums, and Product. Chain Conditionson Ideals. IFP Ideals.Prime Ideals in Near Rings: Prime Ideals. DifferentPrime Ideals. Characterization of Prime Ideals. PrimeRadical. Semiprime Ideals. Nil and Nilpotent Ideals.Dimension and Decompositions in Near Rings:Uniform and Essential Ideals. Finite GoldieDimension. Dimension Conditions. Some EquivalentConditions. Primary and Tertiary Decompositions.Gamma Near Rings: Definitions and Examples.Ideals of Gamma Near Rings. Prime Ideals, NilpotentIdeals of Gamma Near Rings. Modules over GammaNear Rings (Mr-Groups).Fuzzyness in Near Rings and Gamma Near Rings:Fuzzy Sets and Examples. Fuzzy Ideals of Near Ringsand Other Related Algebras. Fuzzy Prime Ideals.Fuzzy Prime Ideals of Gamma Near Rings. FuzzyIdeals of Mr-Groups.Near Rings and Graphs: Introduction to Graphs.Types of Graphs, Algebra of Graphs. Prime Graphand Graph of Near Ring. Miscellaneous.

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

Coming soon!

QuadraticIrrationalsAn Introduction toClassical NumberTheoryFranz Halter-KochUniversity of Graz, Austria

This work focuses on the number theory of quadraticirrationalities in various forms, including continuedfractions, orders in quadratic number fields, and binary quadratic forms. It presents classical resultsobtained by the famous number theorists Gauss,Legendre, Lagrange, and Dirichlet. Collecting infor-mation previously scattered in the literature, the bookcovers the classical theory of continued fractions,quadratic orders, binary quadratic forms, and classgroups based on the concept of a quadratic irrational.

• Presents special results on binary quadraticDiophantine equations and continued fractions,explicit biquadratic class group characters, thedivisibility of class numbers by 16, F. Merten’sproof of the Gauss duplication theory, and a theory of binary quadratic forms that departsfrom the restriction of fundamental discriminants

• Brings together the classical theory of continued fractions, quadratic orders, binaryquadratic forms, and class groups in a unifiedway based on the concept of a quadratic irrational

• Covers Dirichlet’s theorem on primes in arithmetic progressions and Dirichlet’s classnumber formula

• Reviews the abstract algebra needed to understand the material

• Includes many problems and examples suitablefor graduate-level courses in number theory

Selected Contents:

Review of Elementary Algebra and Number Theory.Quadratic Irrationals. Continued Fractions. QuadraticResidues and Gauss Sums. L-Series and Dirichlet’sPrime Number Theorem. Quadratic Orders. BinaryQuadratic Forms. Cubic and Biquadratic Residues.Class Groups. Bibliography. Index.





Coming soon!

AlgebraicCurves inCryptographySan Ling, Huaxiong Wang, andChaoping XingNanyang TechnologicalUniversity, Singapore

This book systematically addresses the many applica-tions of algebraic geometry to cryptography and coding theory. It provides an introduction to impor-tant concepts and demonstrates how to facilitate thenew and fruitful connections between the two excit-ing 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, andbroadcast encryption. Each chapter illustrates the connections between algebraic geometry and thespecified cryptographic topic and demonstrates howalgebraic geometry is used.

Selected Contents:

Introduction to Algebraic Curves. Introduction toError-Correcting Codes. Elliptic Curves: Mapsbetween Elliptic Curves. The Group E(Fq) and ItsTorsion Subgroups. Computational Considerationson Elliptic Curves. Pairings on an Elliptic Curve.Elliptic Curve Cryptography. Secret SharingSchemes: The Shamir Threshold Scheme. OtherThreshold Schemes. General Secret SharingSchemes. Information Rate. Quasi-Perfect SecretSharing Schemes. Linear Secret Sharing Schemes. …Authentication Codes: Authentication Codes. Boundsfor A-Codes. A-Codes and Error-Correcting Codes.Universal Hash Families and A-Codes. …Frameproof Codes: Construction without AlgebraicGeometry. Asymptotic Bounds and Constructionsfrom Algebraic Geometry. Improvements to theAsymptotic Bound. Key Distribution Schemes: KeyPredistribution. Key Predistribution Schemes withOptimal Information Rates. Linear Key PredistributionSchemes. … Broadcast Encryption and MulticastSecurity: One-Time Broadcast Encryption. MulticastRe-Keying Schemes. Re-Keying Schemes withDynamic Group Controllers. Some Applications fromAlgebraic Geometry. Sequences: Linear FeedbackShift Register Sequences. Constructions of AlmostPerfect Sequences. …

Catalog no. C7946, June 2013, c. 336 pp.ISBN: 978-1-4200-7946-3, $79.95 / £49.99Also available as an eBook

Coming soon!

Handbook ofFinite FieldsGary L. MullenThe Pennsylvania StateUniversity, University Park, USA

Daniel PanarioCarleton University, Ottawa,Ontario, Canada

Finite fields provide an enabling background forimportant applications in electrical engineering, com-puter science, physics, and even biology. While newdevelopments have emerged in recent years, manyresearchers still use old problem-solving methods thatoften lead to inaccurate results and solutions.

Poised to become the standard in the field, this state-of-the-art handbook covers all the theoretical aspectsof finite fields and presents numerous applications tocommunications, coding theory, cryptography, ellip-tic curves, computer science, and physics. The firstpart of the book spans the history of finite fieldsthrough the eighteenth and nineteenth centuries. The second part examines theoretical properties offinite fields while the third part discusses importantapplications, both mathematical and practical.

• Covers nearly all theoretical aspects of the subject

• Includes many applications from the fields ofcomputer science and physics

• Presents the most important results for eachtopic without using proofs

• Contains over 3,000 references to enable morein-depth study

Selected Contents:

INTRODUCTION: History of Finite Fields.Introduction to Finite Fields. THEORETICAL PROPER-TIES: Irreducible Polynomials. Primitive Polynomials.Bases. Exponential and Character Sums. Equationsover Finite Fields. Permutation Polynomials. SpecialFunctions over Finite Fields. Sequences over FiniteFields. Algorithms. Curves over Finite Fields.Miscellaneous Theoretical Topics. APPLICATIONS:Combinatorial. Algebraic Coding Theory.Cryptography. Miscellaneous Applications.Bibliography. Index.





Coming soon!

DiscreteStructures andTheirInteractionsJason I. BrownDalhousie University, Halifax,Nova Scotia, Canada

This text is intended for graduate and upper-levelundergraduate students in mathematics who havetaken an initial course in discrete mathematics orgraph theory. The text introduces a number of dis-crete structures, such as hypergraphs, finite topolo-gies, preorders, simplicial complexes, and order idealsof monomials, that most graduate students in combi-natorics, and even some researchers in the field, seldom experience.

The author explains how the discrete structures haveimportant applications in many areas inside and outside of combinatorics. He also shows how to rec-ognize valuable research connections through thesestructures.

• Emphasizes the connections between differentstructures and fields

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

• Contains a variety of exercises that not onlyhighlight the textual material but also encourage students to pursue research-levelwork

Selected Contents:

Introduction. Discrete Structures—A CommonFramework. Graphs and Directed Graphs. Preordersand Partial Orders. Hypergraphs. Complexes andMulticomplexes. Research Problems. Bibliography.Selected Solutions. Appendices. Index.

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

Coming soon!

AlgebraicNumber Fieldsand TheirCompletionsNancy ChildressArizona State University, Tempe,USA

This book integrates local and global theory to reflecta very modern view of algebraic number theory. This approach is used whenever possible to make thebook as accessible as possible to readers with somebackground in abstract algebra.

The author uses contemporary notation and includesnumerous examples and end-of-chapter exercises.Suitable for a course on algebraic number theory or asbackground reading on class field theory, the text cov-ers localization, ramification theory, norms, Minkowskitheory, the unit group, cyclotomic fields, andDedekind domains.

• Integrates the treatment of local and global theories

• Serves as a reference for advanced cryptography

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

• Includes exercises and examples

Selected Contents:

Algebraic Integers

Dedekind Domains

Localization

Ramification Theory

p-adic Numbers

Local Fields and Ramification

Norms

Different and Discriminant

Minkowski Theory

The Unit Group

Cyclotomic Fields

Abelian Extensions of Q





Coming soon!

Handbook ofGraph DrawingandVisualizationEdited by

Roberto TamassiaBrown University, Providence,Rhode Island, USA

This handbook provides a comprehensive survey ofthe field, from its combinatorial and geometric foundations to its applications in various areas of thephysical, life, and social sciences. It offers in-depthcoverage of combinatorial, geometric, and algorith-mic foundations.

With contributions from leading researchers in thefield, the book presents numerous graph drawingalgorithms as well as graph drawing systems.Applications to mathematics, computer science education, software engineering, database systems,artificial intelligence, telecommunications, bioinfor-matics, economics, and sociology are also included.

• Provides a thorough account of graph drawingand visualization

• Presents detailed coverage of combinatorial,geometric, and algorithmic foundations

• Includes applications to computer science andbioinformatics

Selected Contents:

Combinatorial, Geometric, and AlgorithmicFoundations

Graph Drawing Algorithms

Graph Drawing Systems

Applications

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

Coming soon!

Handbook ofGraph TheorySecond EditionEdited by

Jonathan L. GrossColumbia University, New York,New York, USA

Jay YellenRollins College, Winter Park,Florida, USA

Ping ZhangWestern Michigan University, Kalamazoo, USA

Praise for the First Edition:

“… a fine guide to various literatures, especially for topics like Ramsey theory … . Many first-ratemathematicians have contributed, making the exposition’s quality high overall. …. Highly recom-mended.”

—CHOICE, January 2005

The most comprehensive single-source guide tograph theory, the new edition of this bestselling hand-book covers the most current significant topics ingraph theory. Designed with non-experts in mind,this unified, authoritative book makes informationeasy to find and easy to understand. Each chapterincludes lists of definitions and facts accompanied byexamples, 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 optimizationapproaches of graph theory as well as “pure”graph theory

• Unifies the diversity of graph theory terminology and notation

• 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 GraphTheory. Topological Graph Theory. Analytic GraphTheory. Graphical Measurement. Graphs inComputer Science. Networks and Flows.





Coming soon!

Handbook ofLinear AlgebraSecond EditionEdited by

Leslie HogbenIowa State University, Ames, USA

Updated and expanded, the second edition of thiswidely praised bestseller provides comprehensive coverage of linear algebra concepts, applications, andcomputational software packages in an easy-to-usehandbook format. It guides readers from the very elementary aspects of the subject to the frontiers ofcurrent research. The book encompasses the funda-mentals of linear algebra, combinatorial and numeri-cal linear algebra, and applications of linear algebra tovarious disciplines.

• Presents both basic and advanced linear algebra concepts, such as matrix perturbationtheory and inverse eigenvalue problems

• Uses matrix notation throughout the text

• Covers combinatorial and numerical linear algebra

• Explores mathematical and nonmathematicalapplications, such as quantum computing, control theory, signal processing, and computational biology

• Discusses software packages useful for linearalgebra computations, including MATLAB®,Maple™, and Mathematica®

• Provides numerous references for additionalinformation along with a glossary that covers allmajor linear algebra terminology

Selected Contents:

Basic Linear Algebra. Matrices with SpecialProperties. Advanced Linear Algebra. Topics inAdvanced Linear Algebra. Matrices and Graphs.Topics in Combinatorial Matrix Theory. NumericalMethods for Linear Systems. Numerical Methods forEigenvalues. Computational Linear Algebra.Applications to Optimization. Applications toProbability and Statistics. Applications to Analysis.Applications to Physical and Biological Sciences.Applications to Computer Science. Applications toGeometry. Applications to Algebra. InteractiveSoftware for Linear Algebra. Packages of Subroutinesfor Linear Algebra.


Coming soon!

Introduction to ModernCryptographySecond EditionJonathan KatzUniversity of Maryland, CollegePark, USA

Yehuda LindellBar-Ilan University, Ramat Gan,Israel

This updated and expanded second edition of a laud-ed text provides a rigorous yet accessible account ofmodern cryptography, focusing on formal definitions,assumptions, and rigorous proofs of security. The firsthalf of the book gives an extensive treatment of pri-vate-key cryptography, including encryption, mes-sage authentication, and design principles for blockciphers. The second half focuses on public-key cryp-tography, including number theory; the RSA, Diffie-Hellman, and El Gamal cryptosystems; public-keyencryption and digital signatures; and the randomoracle 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 oraclemodel—topics not often found in other texts

• Contains suggestions for further reading as well as numerous exercises at the end of eachchapter

Selected Contents:

Introduction. Perfectly Secret Encryption. Private-KeyEncryption and Pseudorandomness. MessageAuthentication Codes and Collision-Resistant HashFunctions. Practical Constructions of PseudorandomPermutations (Block Ciphers). TheoreticalConstructions of Pseudorandom Objects. NumberTheory and Cryptographic Hardness Assumptions.Factoring and Computing Discrete Logarithms.Private-Key Management and the Public-KeyRevolution. Public-Key Encryption. Additional Public-Key Encryption Schemes. Digital Signature Schemes.Public-Key Cryptosystems in the Random OracleModel. Appendices. Index.

Catalog no. K16475, September 2013, 640 pp.ISBN: 978-1-4665-7026-9, $79.95 / £40.99Also available as an eBook




DiscreteMathematicswith Duckssarah-marie belcastroResearch Associate, Smith College, Northampton,Massachusetts, USA

“When I used Discrete Mathematics with Ducks inclass, I assigned readings and my students came toclass full of questions and ideas. … these classeswere a highlight of my teaching career. I give a lotof credit to this book, thanks to the author’s skill atblending rigor, great examples, casual humor, andprecise writing.”

—David Perkins, author of Calculus and Its Origins

“I think the discovery/exploratory/problem-solvingapproach is ABSOLUTELY the way this course shouldbe taught, and of all the discrete books I have lookedat, this text does the best job of supporting that kindof approach to the subject while still giving enoughof the material in writing to fill in the gaps. … Ifound that the material provided and the instructornotes cut down on my prep time, and I definitelyreferred to them. Having the in-class activitiesincluded is a huge benefit to this book.”

—Dana Rowland, Merrimack College

“… an incredible book … readable by students, use-ful for instructors, and constructed with style andflair. This book will make it much easier to teach anexciting, student-centered discrete mathematicscourse that will also serve as an excellent introduc-tion 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 andPermutations. 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 / £39.95Also available as an eBook

New!

New Directionsof ModernCryptographyZhenfu CaoShanghai Jiao Tong University,China

This volume presents the fundamental definitions,precise assumptions, and rigorous security proofs ofcryptographic primitives and related protocols. It alsodescribes how they originated from security require-ments and how they are applied. The author providesvivid demonstrations of how modern cryptographictechniques can be used to solve security problems.The applications cover wired and wireless communi-cation networks, satellite communication networks,multicast/broadcast and TV networks, and newlyemerging networks. The book also.

• Introduces the latest modern cryptographies,including proxy re-cryptography, attribute-based cryptography, batch cryptography, andnoncommutative cryptography

• Emphasizes the core idea that cryptography isborn and developed for the application requirements

• Presents applications of modern cryptographiesto show their practical value in everyday life

• Addresses some open problems that challengethe new directions of cryptography

Selected Contents:

Introduction: Trust Problem. Ciphertext AccessControl Problem. Efficiency Problems in Multi-Message Cryptology. The Challenges from Quantumand Biological Computing. Organization. Proxy Re-Cryptography: Introduction. Proxy Re-Signature.Proxy Re-Encryption. Attribute-BasedCryptography: Universal Definitions. BoundedCiphertext-Policy Encryption Schemes. Multi-Authority Encryption Schemes. Interval EncryptionSchemes. Fuzzy Identity-Based Signature Schemes.Batch Cryptography: Aggregate Signature andBatch Verification. Batch Decryption and Batch KeyAgreement. Batch RSA’s Implementation Based onDiophantine Equations. Solving the DiophantineEquations. Noncommutative Cryptography: Braid-Based Cryptography. Z-Modular Method. UsingMonomials in Z-Modular Method. Improved KeyExchange over Thompson’s Group. Perspectives.Appendices.

Catalog no. K14392, December 2012, 400 pp.ISBN: 978-1-4665-0138-6, $99.95 / £63.99Also available as an eBook




Combinatoricsof Set PartitionsToufik MansourUniversity of Haifa, Israel

Focusing on a very active area of mathematicalresearch in the last decade, this book presents meth-ods used in the combinatorics of pattern avoidanceand pattern enumeration in set partitions. Each chap-ter gives historical perspectives, contrasts differentapproaches, and illustrates methods and definitionswith worked examples and Maple™ code. The textalso explores research directions and includes end-of-chapter problems that often draw on real-world data.C++ programs and output tables are listed in theappendices and available for download online.

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

• Presents several links between set partitions andareas of mathematics and physics

• Describes a variety of tools and approaches useful in other topics of enumerative combinatorics

• Includes open questions for further research orprojects as well as an extensive bibliography

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

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

Selected Contents:

Introduction. Basic Tools of the Book. GeneratingFunctions. Preliminary Results on Set Partitions.Subword Statistics on Set Partitions. NonsubwordStatistics on Set Partitions. Avoidance of Patterns inSet Partitions. Multi Restrictions on Set Partitions.Asymptotics and Random Set Partition. Gray Codes,Loopless Algorithms and Set Partitions. Set Partitionsand Normal Ordering. Appendices. Bibliography.Index.

Catalog no. K12931, July 2012, 516 pp.ISBN: 978-1-4398-6333-6, $99.95 / £63.99Also available as an eBook

Handbook ofFinite StateBased ModelsandApplicationsEdited by

Jiacun WangMonmouth University, West LongBranch, New Jersey, USA

Applicable to any problem that requires a finite num-ber of solutions, finite state based models (also calledfinite state machines or finite state automata) havefound wide use in various areas of computer scienceand engineering. This handbook provides a completecollection of introductory materials on finite state the-ories, algorithms, and the latest domain applications.For beginners, the book is a handy reference for quick-ly looking up model details. For more experiencedresearchers, it is suitable as a source of in-depth studyin this area.

• Provides extensive coverage of theory and building blocks

• 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

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

Selected Contents:

Finite Automata. Large-Scale Regular ExpressionMatching on FPGA. Finite State Transducers. TreeAutomata. Timed Automata. Quantum FiniteAutomata. Finite Automata Minimization.Incremental Construction of Finite-State Automata.Esterel and the Semantics of Causality. Regular PathQueries on Graph-Structured Data. Applying TimedAutomata to Model Checking of Security Protocols.Optimal Adaptive Pattern-Matching Using FiniteState Automata. Finite State Automata in Compilers.Finite State Models for XML Processing. Petri Nets.Statecharts. Model Checking. System Modeling withUML State Machines. Index.

Catalog no. K12067, October 2012, 409 pp.ISBN: 978-1-4398-4618-6, $99.95 / £63.99Also available as an eBook




Combinatoricsof PermutationsSecond EditionMiklós BónaUniversity of Florida, Gainesville,USA

“… an excellent book on an important subject.”—Fernando Q. Gouvêa, MAA Reviews, December 2012

(This book is in the MAA’s basic library list.)

“… a comprehensive, engaging, and eminentlyreadable introduction to all aspects of the combina-torics of permutations. The chapter on patternavoidance is especially timely and gives the first sys-tematic treatment of this fascinating and active areaof research. This book can be utilized at a variety oflevels, from random samplings of the treasures there-in to a comprehensive attempt to master all thematerial and solve all the exercises. In whateverdirection the reader’s tastes lead, thorough enjoy-ment and appreciation of a beautiful area of combi-natorics are certain to ensue.”

—From the Foreword by Richard Stanley, MIT

A 2006 CHOICE Outstanding Academic Title, the firstedition of this bestseller was lauded for its detailed yetengaging treatment of permutations. With much ofthe book significantly revised and expanded, this sec-ond edition includes new material on alternating per-mutations, multivariate applications, pattern avoid-ance, and asymptotically normal distributions. It alsocontains a new chapter on three sorting algorithmsfrom molecular biology.

Selected Contents:

In One Line and Close. Permutations as LinearOrders. In One Line and Anywhere. Permutations asLinear Orders. Inversions. In Many Circles.Permutations as Products of Cycles. In Any Way butThis. Pattern Avoidance. The Basics. In This Way butNicely. Pattern Avoidance. Follow-Up. Mean andInsensitive. Random Permutations. Permutations ver-sus Everything Else. Algebraic Combinatorics ofPermutations. Get Them All. Algorithms andPermutations. How Did We Get Here? Permutationsas Genome Rearrangements. Solutions to Odd-Numbered Exercises. References. List of FrequentlyUsed Notation. Index.


CryptologyClassical and Modernwith MapletsRichard E. KlimaAppalachian State University,Boone, North Carolina, USA

Neil P. SigmonRadford University, Virginia, USA

“All told, the authors have done an admirable job ofbalancing the competing goals of producing a textthat can be read by people with limited mathemat-ics background, but at the same time is maintainedat a college level. This is not ‘cryptology for dum-mies,’ watered down to the point of uselessness, butis instead a book that, though accessible, requiresan appropriate amount of effort and thought on thepart of the reader. … This is a book that not onlymeets but exceeds its goal of being a suitable text fora course in cryptology for non-majors. It is highlyrecommended for anybody teaching such a course,and it certainly belongs in any good universitylibrary.”

—Mark Hunacek, MAA Reviews, September 2012

In a clear, nontechnical manner, this text explains howfundamental mathematical concepts are the bases ofcryptographic algorithms. It covers the Enigmamachine and Navajo code used during World War II,describes the implementation and cryptanalysis ofclassical ciphers, and gives straightforward explana-tions of the AES, public-key ciphers, and messageauthentication. The book assumes minimal mathe-matical prerequisites and incorporates easy-to-useMaplets throughout that provide practical examplesof the techniques. The Maplets are available for down-load online.

Selected Contents:

Introduction to Cryptology. Substitution Ciphers.Transposition Ciphers. The Enigma Machine andNavajo Code. Shift and Affine Ciphers. Alberti andVigenère Ciphers. Hill Ciphers. RSA Ciphers. ElGamalCiphers. The Advanced Encryption Standard.Message Authentication. Bibliography. Hints orAnswers to Selected Exercises. Index.





TranscendentalRepresentationswithApplications to Solids andFluidsL.M.B.C. CamposLisbon Technical University,Portugal

Building on the author’s previous book ComplexAnalysis with Applications to Flows and Fields, this workfocuses on four infinite representations: series expan-sions, series of fractions for meromorphic functions,infinite products for functions with infinitely manyzeros, and continued fractions as alternative represen-tations. The book also continues the application ofcomplex functions to more classes of fields, includingincompressible rotational flows, compressible irrota-tional flows, unsteady flows, rotating flows, surfacetension and capillarity, deflection of membranesunder load, torsion of rods by torques, plane elastici-ty, and plane viscous flows.

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

• Unifies interdisciplinary topics of physics, mathematics, and engineering

• Explores the interplay between physical laws andmathematical methods as a basis for modelingnatural phenomena and engineering devices

• Includes examples of applications with interpretation of results and discussion ofassumptions and their consequences

• Enables readers to construct mathematical-physical models suited to new observations ornovel engineering devices

• Contains many illustrations, tables, and diagrams that clarify the links between topics

Selected Contents:

Sequences of Fractions or Products. Compressibleand Rotational Flows. Exponential and LogarithmicFunctions. Plane Elasticity and MultiharmonicFunctions. Circular and Hyperbolic Functions.Membranes, Capillarity, and Torsion. Infinite andCyclometric Representations. Confined and UnsteadyFlows. Infinite Processes and Summability. TwentyExamples. Bibliography. Index.

Catalog no. K11546, April 2012, 898 pp.ISBN: 978-1-4398-3431-2, $149.95 / £89.00Also available as an eBook

CombinatorialScientificComputingEdited by

Uwe NaumannRWTH Aachen University,Germany

Olaf SchenkUniversity of Lugano, Switzerland

This volume explores the latest research on creatingalgorithms and software tools to solve key combina-torial problems on large-scale high-performance com-puting architectures. It focuses on load balancing andparallelization, large-scale optimization, algorithmicdifferentiation of numerical simulation code, sparsematrix software tools, and combinatorial challengesand applications in large-scale social networks. Theauthors unify these seemingly disparate areas througha common set of abstractions and algorithms.

• Provides an overview of modern combinatorialgraph algorithms in computational science

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

• Focuses on discrete data structures in computa-tional science, such as hypergraph partitioning,vertex and edge reordering and coloring, andbipartite graph matching

• Presents applications of high-performance scientific computing in biomedicine, fluiddynamics, and social science

Selected Contents:

Combinatorial Scientific Computing: Past Successes,Current Opportunities, Future Challenges.Combinatorial Problems in Solving Linear Systems.Combinatorial Preconditioners. Scalable HybridLinear Solvers. Combinatorial Problems inAlgorithmic Differentiation. Combinatorial Problemsin OpenAD. Getting Started with ADOL-C.Algorithmic Differentiation and NonlinearOptimization for an Inverse Medium Problem.Combinatorial Aspects/Algorithms in ComputationalFluid Dynamics. Unstructured Mesh Generation. 3DDelaunay Mesh Generation. Two-DimensionalApproaches to Sparse Matrix Partitioning. ParallelPartitioning, Ordering, and Coloring in ScientificComputing. Scotch and PT-Scotch GraphPartitioning Software: An Overview. …

Catalog no. K11349, January 2012, 600 pp.ISBN: 978-1-4398-2735-2, $89.95 / £57.99Also available as an eBook




Applications ofCombinatorialMatrix Theoryto LaplacianMatrices ofGraphsJason J. MolitiernoSacred Heart University, Fairfield,Connecticut, USA

“… this book works well as a reference textbook forundergraduates. Indeed, it is a distillation of a num-ber of key results involving, specifically, theLaplacian matrix associated with a graph (which issometimes called the ‘nodal admittance matrix’ byelectrical engineers). … a well-written source ofbackground on this growing field. The sources aresome of the seminal ones in the field, and the bookis 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 / £57.99Also available as an eBook

Coming soon!

Parallel GraphAlgorithmsEdited by

David A. BaderGeorgia Institute of Technology,Atlanta, USA

To efficiently solve large-scale graph problems, it isnecessary to design high-performance computing systems and novel parallel algorithms. In this book,some of the world’s most renowned experts explorethe latest research and applications in this importantarea. The book covers benchmarks, programming,architecture, and applications. It presents the theoret-ical foundations of graph theory and graph algo-rithms and describes applications in social networkanalysis, machine learning, biology, map routing, andmore.

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

Coming soon!

The Handbookof GraphAlgorithms andApplications Volume I: Theory andOptimizationKrishnaiyan Thulasiraman, Tako Nishizeki, and Guoliang XueFocusing on design, proof of correctness, and com-plexity analysis, the first volume presents a detaileddiscussion of algorithms that are useful in a variety ofapplications and provides an authoritative review ofthe current state of the art. Using figures to help illus-trate the concepts, the book examines topics, such asincremental algorithms and online algorithms, thathave yet to receive much attention but have greatpotential for future applications.

Catalog no. C5955, November 2013, 1216 pp.ISBN: 978-1-58488-595-5, $129.95 / £82.00Also available as an eBook

Volume II:ApplicationsKrishnaiyanThulasiraman, Arun Kumar Somani,and Sarma VrudhulaThe second volume focuses on a wide range of algorithmic applications, including graph theoryproblems. It emphasizes new algorithms andapproaches that have been triggered by applications.The book requires minimal exposure to related tech-nologies in order to understand the various approach-es. Each chapter is devoted to a single applicationarea, from VLSI circuits to optical networks to program graphs, and features an introduction by apioneering researcher in that particular field.

Catalog no. C5971, November 2013, 1024 pp.ISBN: 978-1-58488-597-9, $119.95 / £76.99Also available as an eBook






Encompassing over 60 books, the Discrete Mathematics andIts Applications series edited by Kenneth H. Rosen publishes

leading references, handbooks, and textbooks, includingCryptography: Theory and Practice, Third Edition by

Douglas R. Stinson and the Handbook of Linear Algebraedited by Leslie Hogben (new edition coming soon).

If you have a book proposal for this series, email publisher Sunil Nair at [email protected].

CRC Press/Taylor & Francis6000 Broken Sound Parkway NW, Suite 300

Boca Raton, FL 33487, USA

Call for Authors



6000

Bro

ken

Soun

d Pa

rkw

ay, N

W, S

uite

300

Boca

Rat

on, F

L 33

487,

USA

Page

3Pa

ge 6

Page

10

Fo

r a c

om

ple

te li

st o

f M

ath

em

atic

s b

oo

ks,

ple

ase

vis

it w

ww

.crc

pre

ss.c

om




Documents

Discrete Mathematics and Combinatorics