Discrete Mathematics

The Most Essential Books in

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Contents Bestsellers ................................................................3 Forthcoming Books..................................................7 Our Full Range of Titles ..........................................9

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Bestsellers Handbook of Graph Theory Second Edition

Handbook of Graph Drawing and Visualization

Edited by

Edited by

Jonathan L. Gross, Jay Yellen, and Ping Zhang

Roberto Tamassia

With 34 new contributors, this best-selling handbook provides comprehensive coverage of the main topics in pure and applied graph theory. This second edition— over 400 pages longer than its predecessor—incorporates 14 new sections. Each chapter includes lists of essential definitions and facts, accompanied by examples, tables, remarks, and, in some cases, conjectures and open problems. A bibliography at the end of each chapter provides an extensive guide to the research literature and pointers to monographs. This edition also contains notes regarding terminology and notation.

“In the topological and geometric foundations to graph drawing, this collection goes beyond defining planarity or even minimizing edge crossings, discussing also spine, radial, circular, tree, and rectangular drawing definitions and algorithms. There is much content on formally defining and approaching such subjective and even aesthetic areas as legibility in name placement and labeling, as well as maximizing pleasing symmetries and other methods related to edge lengths and linearity that research has shown to impart information to humans effectively.”

• Covers new topics in pure and applied graph theory • Includes 65 self-contained chapters organized into 13 parts • Bridges theory and practice with many easy-to-read algorithms • Unifies the diversity of graph theory terminology and notation • Provides a glossary and references at the end of each chapter

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.

Communication Networks. Natural Science and Processes. Index.

Catalog no. K13767, December 2013, 1630 pp.

ISBN: 978-1-4398-8018-0, $139.95 / £89.00 Also available as an eBook

Brown University, Providence, Rhode Island, USA

—Tom Schulte, MAA Reviews, February 2014

“…an impressive compendium of research [on] … algorithms, layout strategies, and software for diverse problem domains. It’s great to have all these resources in one place, showing the vibrant activity in graph drawing and visualization. The book lays a foundation for the next generation of research breakthroughs. Whether you drill down or go wide, you’ll learn something useful. You’ll see how effectively designed network visualizations can produce powerful insights in many fields.”

—Ben Shneiderman, University of Maryland

Selected Contents: Planarity Testing and Embedding. Crossings and Planarization. Symmetric Graph Drawing. Proximity Drawings. Tree Drawing Algorithms. Planar StraightLine Drawing Algorithms. Planar Orthogonal and Polyline Drawing Algorithms. Spine and Radial Drawings. Circular Drawing Algorithms. Rectangular Drawing Algorithms. Simultaneous Embedding of Planar Graphs. Force-Directed Drawing Algorithms.

Hierarchical Drawing Algorithms. Three-Dimensional Drawings. Labeling Algorithms. Graph Markup Language (GraphML). The Open Graph Drawing Framework (OGDF). GDToolkit. PIGALE. Biological Networks. Computer Security. Graph Drawing for Data Analytics. Graph Drawing and Cartography.

Graph Drawing in Education. Computer Networks.

Social Networks. Index.

Catalog no. C4126, August 2013, 862 pp.

ISBN: 978-1-58488-412-5, $99.95 / £63.99

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Bestsellers Handbook of Linear Algebra Second Edition

Discrete Mathematics with Ducks

Edited by

sarah-marie belcastro

Leslie Hogben

Research Associate, Smith College, Northampton, Massachusetts, USA

Iowa State University, Ames, USA

“The second edition is substantially expanded … A huge amount of thought has gone into the book. … Leslie Hogben has done an outstanding job to produce a book of this size in a uniform style with such a high standard of editing and typesetting. … this is certainly a book to ask your library to order and maybe even to purchase yourself.”

—Nick Higham (University of Manchester) on His Blog, March 2014

With a substantial amount of new material, this bestselling handbook provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides readers from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition includes 20 new chapters that cover combinatorial matrix theory topics, numerical linear algebra topics, more applications of linear algebra, the use of Sage for linear algebra, and much more.

• 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, computational biology, and epidemiology • Discusses software packages useful for linear algebra computations, including Sage, MATLAB®, Maple™, and Mathematica® • Provides numerous references for additional information along with a glossary that covers all major linear algebra terminology

Selected Contents: Linear Algebra. Combinatorial Matrix Theory and Graphs. Numerical Methods. Linear Algebra in Other Disciplines. Computational Software. Index.

Catalog no. K14662, November 2013, 1904 pp.

ISBN: 978-1-4665-0728-9, $169.95 / £108.00 Also available as an eBook

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“This book can certainly be used to teach the standard course in discrete mathematics designed for computer science majors. The lighter touch of duck references does amuse you and does not ever overshadow or disguise the mathematical concepts.”

—Charles Ashbacher, MAA Reviews, August 2012

“When I used Discrete Mathematics with Ducks in class, I assigned readings, and my students came to class full of questions and ideas. … 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.”

—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, $62.95 / £41.99 Also available as an eBook

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Bestsellers Handbook of Finite Fields Gary L. Mullen The Pennsylvania State University, University Park, USA

Daniel Panario Carleton University, Ottawa, Ontario, Canada

Poised to become the leading reference in the field, this definitive handbook is exclusively devoted to the theory and applications of finite fields. Edited by two renowned researchers and with more than 80 international contributors compiling state-of-the-art research, the book uses a uniform style and format throughout and each chapter is self contained and peer reviewed. The handbook provides a comprehensive index and easy access to over 3,000 references, enabling readers to quickly locate up-todate facts and results regarding finite fields.

• Gives a complete account of state-of-the-art theoretical and applied topics in finite fields • Describes numerous applications from the fields of computer science and engineering • Presents the history of finite fields and a brief summary of basic results • Discusses theoretical properties of finite fields • Covers applications in cryptography, coding theory, and combinatorics • Includes many remarks to further explain the various results • Contains more than 3,000 references, including citations to proofs of important results • Offers extensive tables of polynomials useful for computational issues, with even larger tables available on the book’s CRC Press web page

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, 1068 pp.

ISBN: 978-1-4398-7378-6, $139.95 / £89.00 Also available as an eBook

Secret History The Story of Cryptology Craig P. Bauer York College of Pennsylvania, USA

“Every once and a while a book appears that has a significant impact on the field of cryptologic history. David Kahn’s The Codebreakers and F.L. Bauer’s Decrypted Secrets are two such books. Secret History now joins that collection. …

Bauer has merged cryptologic history with the mathematical foundations of cryptology in a correct, understandable, and enthusiastic presentation.

Secret History is an excellent choice for a historian of cryptology, a teacher of cryptology, or anyone who wants to get a glimpse of cryptology.”

—Chris Christensen, Cryptologia

“… one of the most engaging storytelling adventures on the evolution of secret keeping. … The math behind the systems described, while present, is never obscured by the fascinating setting in which it was developed. This is the way in which cryptography, one of the most difficult applications of discrete mathematics, was meant to be learned, with real-life cloak-and-dagger intrigue. Highly recommended.”

—T.D. Richardson, CHOICE, 2013

“It is by far the clearest and most comprehensive of the books dealing with the new cryptology, including of course the classic ciphers and some of the important historical ones … the book provides what I was unable to give cryptology—a mathematical underpinning to it all. … All of us in the cryptology community are grateful to [Bauer] for it.”

—David Kahn, Historian, and Author of The Codebreakers

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, March 2013, 620 pp.

ISBN: 978-1-4665-6186-1, $69.95 / £44.99

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Bestsellers Combinatorics of Permutations Second Edition Miklós Bóna University of Florida, Gainesville, USA

“The extended new edition of Bóna’s textbook will continue to provide a wealth of information on the combinatorial facet of permutations, to both students and researchers in the subject.”

—Martin Kiazar, Mathematical Review Clippings

“There is a new chapter nine, ‘devoted to sorting algorithms whose original motivation comes from molecular biology.’ Chapters 1, 3, 4, and 6 have been ‘significantly changed and expanded’ and all chapters have new exercises and problems … an excellent book on an important subject.”

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

Catalog no. K12299, June 2012, 478 pp.

ISBN: 978-1-4398-5051-0, $93.95 / £59.99 Also available as an eBook

Discrete Dynamical Systems and Chaotic Machines Theory and Applications Jacques M. Bahi and Christophe Guyeux University of Franche-Comté, Belfort

Until the authors’ recent research, the practical implementation of the mathematical theory of chaos on finite machines raised several issues. This self-contained book shows how to make finite machines, such as computers, neural networks, and wireless sensor networks, work chaotically as defined in a rigorous mathematical framework. Taking into account that these machines must interact in the real world, the authors share their research results on the behaviors of discrete dynamical systems and their use in computer science.

• Provides full explanations and illustrative examples of the construction of truly chaotic finite machines • Explains the similarities and differences between chaos and randomness

Introduction to Cryptography with OpenSource Software Alasdair McAndrew Victoria University, Melbourne, Australia

“This very well-written book is recommended to graduate or final-year undergraduate students intended to start research work on both theoretical and experimental cryptography. Most of the cryptographic protocols are illustrated by various examples and implemented using the open-source algebra software Sage. The book provides a rigorous introduction to the mathematics used in cryptographic and covers almost all modern practical cryptosystems. … a valuable resource for practitioners looking for experimental cryptography with a computer algebra system.”

• Examines the relationship between chaos and security as well as chaos and randomness • Discusses when to use chaos for computer security • Illustrates how to build completely secured wireless sensor networks using chaos

Selected Contents: An Introduction to Chaos: Classical Examples by Way of Introduction. The Mathematical Theory of Chaos: Definitions and Notations. Devaney’s Formulation of Chaos. Other Formulations of Chaos.

From Theory to Practice: A Fundamental Tool: the Chaotic Iterations. Theoretical Proofs of Chaotic Machines. Applications of Chaos in the Computer Science Field: Information Security. Wireless Sensor Networks. Conclusion: Conclusion. Bibliography.

Index.

Catalog no. K15321, June 2013, 230 pp.

ISBN: 978-1-4665-5450-4, $89.95 / £57.99 Also available as an eBook

—Abderrahmane Nitaj, IACR book reviews, February 2014

Catalog no. K11232, May 2011, 461 pp.

ISBN: 978-1-4398-2570-9, $83.95 / £51.99

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Forthcoming Books Quantitative Graph Theory Mathematical Foundations and Applications Edited by

Matthias Dehmer and Frank Emmert-Streib This book presents methods for analyzing graphs and networks quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical techniques, it covers a wide range of quantitative graph-theoretical concepts and methods, including those pertaining to random graphs. Through its broad coverage, the book fills a gap in the contemporary literature of discrete and applied mathematics, computer science, systems biology, and related disciplines.

• Provides the first book on quantitative graph theory • Highlights the importance of quantitative methods in graph and network theory • Includes comprehensive coverage of both theory and practice

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

Yehuda Lindell Bar-Ilan University, Ramat Gan, Israel

This updated and expanded second edition of a highly praised 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 publickey cryptography, including number theory; the RSA, Diffie-Hellman, and El Gamal cryptosystems; publickey encryption and digital signatures; and the random oracle model and its applications.

Catalog no. K16475, November 2014, 600 pp.

ISBN: 978-1-4665-7026-9, $79.95 / £40.99 Also available as an eBook

Selected Contents: Network Centrality and Social Movement Media Coverage: A Two-Mode Network Analytic Approach.

Three Measures of Edge-Uncolorability. Betweenness Centrality, Estimates, and Relations to Other Graph Invariants. Graph Complexity of Chemical Compounds in Biological Pathways. The Wiener Index for Some Classes of Hexagonal Chains. On Digraph Width Measures. Two New Graph Kernels and Their Application to Chemoinformatics: Network Topology Measures. Wide Diameter of Cartesian Graph Bundles. On Properties of Quantitative Network Measures. Graph Theoretic Approach to Complex Systems Engineering. All Normalized AntiMonotonic Overlap Graph Measures Are Bounded.

Catalog no. K19041, October 2014, c. 464 pp.

ISBN: 978-1-4665-8451-8, $99.95 / £63.99 Also available as an eBook

Parallel Graph Algorithms Edited by

David A. Bader Graph theoretic problems are representative of fundamental kernels in traditional and emerging scientific applications, such as complex network analysis, data mining, and computational biology, as well as applications in national security. 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.

Catalog no. K16641, February 2015, c. 400 pp.

ISBN: 978-1-4665-7326-0, $89.95 / £57.99 Also available as an eBook

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Forthcoming Books Introduction to Closure Systems Robert E. Jamison Clemson University, South Carolina, USA

The notion of closure pervades mathematics, especially in the fields of topology and projective geometry.

Demonstrating this pervasiveness in the field, this graduate-level book provides a complete introduction to closure systems. With an emphasis on finite spaces and algebraic closures, the text covers graph theory, ordered sets, lattices, projective geometry, and formal logic as they apply to the study of closures. Each chapter presents a vignette to illustrate the topic covered. The author also includes numerous exercises as well as concrete examples to support the material discussed.

• Covers finite spaces along with infinite spaces where applicable • Includes vignettes to provide an introduction to a number of mathematical topics, such as graph coloring • Presents exercises and examples of graph theory, ordered sets, lattices, projective geometry, and formal logic

Selected Contents: An Introduction to Closures. Basic Properties of Closures: Closures Systems and Their Hulls. Hull Operators and the Substitution Property. Filling in Dependencies. Algebraic and Topological Closures.

Closures That Are Both Topological and Algebraic.

Isomorphism and Cryptomorphy. Separation.

Constructions on Closures. Small Closures.

Alignments: Universal Algebras. Realizing Alignments by a Single Operation. Universality of Groupoids. Universality of Napoleonic Closure.

Copoints in Finitary Closures. Copoints and the Separation Axioms 53 and 54. Matroids and Antimatroids. Independence. More Examples of Matroids and Antimatroids. Order Convexity. Acyclic Semigroups. Articulated Sums. Background Review.

Set Theory: Cardinals. The Axiom of Choice.

Ordinals. Countability.

Catalog no. K11049, November 2014, c. 352 pp.

ISBN: 978-1-4398-1991-3, $89.95 / £57.99 Also available as an eBook

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The Handbook of Graph Algorithms and Applications Volume I: Theory and Optimization Krishnaiyan Thulasiraman, Tako Nishizeki, and Guoliang Xue This volume provides comprehensive coverage of basic concepts and recent developments in the field.

Focusing on design, proof of correctness, and complexity analysis, the book 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 incremental algorithms and online algorithms that have yet to receive much attention but have great potential for future applications.

Catalog no. C5955, April 2015, 1216 pp.

ISBN: 978-1-58488-595-5, $129.95 / £82.00 Also available as an eBook

Volume II: Applications Krishnaiyan Thulasiraman, Arun Kumar Somani, and Sarma Vrudhula This volume covers new algorithms and approaches that have been triggered by applications. The approaches discussed require minimal exposure to related technologies in order to understand the material. Each chapter is devoted to a single application area, from VLSI circuits to optical networks to program graphs, and features an introduction by a pioneer researcher in that particular field. The book serves as a single-source reference for graph algorithms and their related applications.

Catalog no. C5971, April 2015, 1024 pp.

ISBN: 978-1-58488-597-9, $119.95 / £76.99 Also available as an eBook

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Our Full Range of Titles Discrete Structures and Their Interactions Jason I. Brown Dalhousie University, Halifax, Canada

“The book is a collection of examples, each of which shows either how discrete structures interact with each other or how discrete structures interact with other parts of mathematics. … I am certain I will use some examples I found in this book when I teach combinatorics in the upcoming semester.”

—Miklós Bóna, MAA Reviews, December 2013

With exercises and research problems, this text highlights the connections among various discrete structures, including graphs, directed graphs, hypergraphs, partial orders, finite topologies, and simplicial complexes. It also explores their relationships to classical areas of mathematics, such as linear and multilinear algebra, analysis, probability, logic, and topology. The author explains how discrete structures have important applications in many areas inside and outside of combinatorics. He also discusses how to recognize valuable research connections through the structures.

• Covers discrete structures from a variety of viewpoints, including combinatorial, algebraic, probabilistic, analytic, and logical • Develops deep connections between different fields of mathematics, encouraging students to think creatively and analytically • Supplies a more general introduction to discrete structures than other texts • Includes extensive end-of-chapter exercises, with selected solutions at the back of the book • Offers suggestions for research projects

Selected Contents: 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.

Catalog no. K16844, June 2013, 224 pp.

ISBN: 978-1-4665-7941-5, $79.95 / £49.99 Also available as an eBook

Algebraic Curves in Cryptography San Ling, Huaxiong Wang, and Chaoping Xing Nanyang Technological University, Singapore

“The book is written in a user-friendly style, with good coverage of the background, many examples, and a detailed bibliography of over 180 items. It is mainly directed towards graduate students and researchers, but some parts of the book are even accessible for advanced undergraduate students. The book is highly recommended for readers interested in the manifold applications of algebraic curves over finite fields.”

—Harald Niederreiter, Mathematical Reviews, March 2014

“The book is filled with examples to illustrate the various constructions and, assuming a basic knowledge of combinatorics and algebraic geometry, it is almost self-contained.”

—Felipe Zaldivar, MAA Reviews, September 2013

This book is one of the first to focus on many topics in cryptography involving algebraic curves. After supplying the necessary background on algebraic curves, the authors discuss error-correcting codes, including algebraic geometry codes, and provide an introduction to elliptic curves. Each chapter in the remainder of the book deals with a selected topic in cryptography (other than elliptic curve cryptography).

• Illustrates various kinds of algebraic curves in a broad range of cryptographic applications, including secret sharing, authentication codes, frameproof codes, key distribution, broadcast encryption, and sequences for stream ciphers • Requires minimal background in advanced mathematics and cryptography • Provides the required fundamentals on algebraic curves • Offers a brief introduction to elliptic curves and applications

Selected Contents: Introduction to Algebraic Curves. Introduction to Error-Correcting Codes. Elliptic Curves and Their Applications to Cryptography. Secret Sharing Schemes. Authentication Codes. Frameproof Codes.

Key Distribution Schemes. Broadcast Encryption and Multicast Security. Sequences. Bibliography. Index.

Catalog no. C7946, June 2013, 340 pp.

ISBN: 978-1-4200-7946-3, $79.95 / £49.99 Also available as an eBook

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Our Full Range of Titles Quadratic Irrationals An Introduction to Classical Number Theory

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

Franz Halter-Koch University of Graz, Austria

“… a cohesive treatment of several important topics in classical number theory by first developing a theory of quadratic irrationals and then building on that to show how the other topics reflect different faces of this theory. … it does include a better selection of numerical examples than is found in most books, and it has a number of applications to other areas such as diophantine equations.”

—Allen Stenger, MAA Reviews, January 2014

“…comprehensive text dealing with the theory of binary quadratic forms. … one of the main interests of this book is that it gathers a lot of important results, which are generally strewn throughout the literature and are quite difficult to access. This text is quite clear and some exercises and examples are scattered throughout the book. I therefore think that it will find many interested readers within the international mathematical community.”

Kuncham Syam Prasad Manipal University, India

“The book is quite self-contained in that the introduction describes the basic concepts covered in the rest of the book, including some notions on fuzzy sets and fuzzy algebraic groups. … The vast majority of the results, even preliminary ones, are accompanied by proofs, making the book quite interesting for readers who want to get acquainted with the theory of near rings.”

—Computing Reviews, October 2013

Suitable for researchers and graduate students, this book provides readers with an understanding of near ring theory and its connection to fuzzy ideals and graph theory. It explores the relationship between near rings and fuzzy sets and between near rings and graph theory. The authors cover topics from recent literature along with several characterizations.

—Olivier Bordellès, Mathematical Reviews, December 2013

• Examines the connections among near rings, fuzzy aspects, and graph theory

• Brings together various aspects of the theory of quadratic irrationals previously scattered in the literature

• Provides a comprehensive compilation of dimension and decomposition theory, including Goldie dimension in near ring modules

• Takes an elementary but rigorous approach to the material from an algebraic point of view

• Includes all the prerequisites, such as the theory of vector spaces and elementary graph theory

• Presents the theory of binary forms and orders in a unified way without restrictions to fundamental discriminants

• Contains detailed results and proofs as well as many illustrations and counterexamples

• Gives the algebraic and number-theoretical prerequisites in a comprehensive appendix • Covers several recent results concerning twoclass groups, biquadratic reciprocity, continued fractions, and binary Diophantine equations

Selected Contents: 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. Appendices. Bibliography. Index.

• Offers references for theorems wherever necessary

Selected Contents: Preliminaries. Fundamentals of Near Rings. More Concepts on Near Rings. Prime and Semiprime Ideals. Dimension and Decomposition Theory. Matrix Near Rings. Gamma Near Rings. Fuzzy Aspects in Near Rings and Gamma Near Rings. Fundamental Concepts of Graph Theory. References. Index.

Catalog no. K13386, May 2013, 480 pp.

ISBN: 978-1-4398-7310-6, $99.95 / £63.99 Also available as an eBook

Catalog no. K20533, June 2013, 431 pp.

ISBN: 978-1-4665-9183-7, $99.95 / £63.99 Also available as an eBook

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Our Full Range of Titles Introduction to Biological Networks Alpan Raval Claremont Graduate University, California, USA

Animesh Ray Keck Graduate Institute, Claremont, California, USA

“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

• 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 current research in biology and medicine

Selected Contents: The Living Interactome. Experimental Inference of Interactions. Prediction of Physical Interactions.

Metabolic Networks and Genetic Interactions.

Testing Inferred Networks. Small Model Networks.

Tractable Models of Large Networks. Network Modularity and Robustness. Networks and Disease.

Catalog no. C4630, April 2013, 335 pp.

ISBN: 978-1-58488-463-7, $79.95 / £49.99 Also available as an eBook

GameTheoretical Models in Biology Mark Broom City University, London, UK

Jan Rychtář University of North Carolina at Greensboro, USA

“… a comprehensive, up-todate introduction that uniquely blends mathematical clarity and biological intuition. … Students of evolutionary game theory … would do well to read Game-Theoretical Models in Biology all the way to the finish line. This engaging primer demonstrates that there is no tension between mathematical elegance and biological fidelity: both are needed to further our understanding of evolution.”

—Benjamin Allen and Martin A. Nowak, Science, August 2013

“Assuming only a modicum of mathematics, Broom and Rychtář lead their readers all the way from the rudiments of evolutionary game theory to the research frontier. … 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.”

—Mike Mesterton-Gibbons, Florida State University

“This book should prove to be 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, University of Sheffield

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, March 2013, 520 pp.

ISBN: 978-1-4398-5321-4, $79.95 / £39.99

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Our Full Range of Titles 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.

With an emphasis on implementation issues, the author 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.

New Directions of Modern Cryptography Zhenfu Cao Shanghai Jiao Tong University, China

This book 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.

Providing vivid demonstrations of how modern cryptographic techniques can be used to solve security problems, the book’s applications cover wired and wireless communication networks, satellite communication networks, multicast/broadcast and TV networks, and newly emerging networks.

• Introduces modern cryptographies: proxy re-cryptography, attribute-based cryptography, batch cryptography, and noncommutative cryptography

• Explores many important computational issues and recent developments in number theory

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

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

• Presents the applications of the latest cryptographies to show their practical value in everyday life

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

• Explores challenges in the future of cryptography

• Describes the application of number theory in public-key cryptography

Selected Contents:

• 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 Also available as an eBook

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, $104.95 / £66.99 Also available as an eBook

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Our Full Range of Titles Handbook of Finite State Based Models and Applications

Combinatorics of Set Partitions

Edited by

“… a comprehensive account of the history and current research in the combinatorics of pattern enumeration and pattern avoidance in set partitions. …

While it is aimed primarily at advanced undergraduate and graduate students in discrete mathematics with a focus on set partitions, its extensive bibliography, with 375 entries, and the variety of constructions and approaches used in the text make it a valuable reference for researchers in this field.”

Jiacun Wang Monmouth University, West Long Branch, New Jersey, USA

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 extensive coverage of theory and building blocks • Includes examples of applications in each chapter • Discusses automata-based programming

Toufik Mansour University of Haifa, Israel

—Ricardo Mamede, Zentralblatt MATH 1261

“… a comprehensive account of recent and current research on the pattern-related aspects of set partitions.”

—David Callan, Mathematical Reviews, April 2013

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

• Presents advanced applications in areas such as FPGA design, graph-structured data query, security protocol model checking, and XML processing

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

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

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

Selected Contents: 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, $104.95 / £66.99 Also available as an eBook

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

• Contains end-of-chapter exercises, with hints and solutions in an appendix • Offers C++ programs and their outputs on the author’s web page

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, $104.95 / £66.99 Also available as an eBook

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Our Full Range of Titles Cryptology

Transcendental Representations with Applications to Solids and Fluids

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

Luis Manuel Braga da Costa Campos

Neil P. Sigmon Radford University, Virginia, USA

“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.”

—Mark Hunacek, MAA Reviews, September 2012

• Illustrates the importance of cryptology in cultural and historical contexts • Describes the implementation and cryptanalysis of classical ciphers • Gives straightforward explanations of the AES, public-key ciphers, and message authentication • Requires no prior programming knowledge or background in college-level mathematics • Integrates the easy-to-use technology of Maplets throughout • Offers material for teaching nonmathematical courses • Provides exercises in each chapter section, including some that can be used as projects • Presents all Maplet-based examples and exercises in separate sections • Supplies Maplet exercises and all of the Maplets used in the text 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, $83.95 / £51.99 Also available as an eBook

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University of Lisbon, Portugal

“… the book will be useful to engineers who do not want to learn so much on mathematical results but who are mostly interested by the resolution of concrete mechanical problems. The length of the book is not a problem as the many tables may help the reader to quickly [find] the solution of the problem he is looking for.”

—Alain Brillard, Zentralblatt MATH

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. This book also continues the application of complex functions to more classes of fields.

• 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 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, $159.95 / £93.00 Also available as an eBook

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Our Full Range of Titles Combinatorial Scientific Computing Edited by

Uwe Naumann RWTH Aachen University, Germany

Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs Jason J. Molitierno

Olaf Schenk University of Lugano, Switzerland

Sacred Heart University, Fairfield, Connecticut, USA

“This text is a deep and—as any scientist working with large datasets will tell you—much-needed treatment of an emerging field, focused specifically on large-scale computing. It is readable and practical and covers areas that have many open problems, making it an excellent resource both for scientific researchers looking for solutions and computing researchers looking for computational and combinatoric problems to solve.”

“… 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.”

—Computing Reviews, May 2013

• Provides an overview of modern combinatorial graph 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 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. Massively Parallel Graph Partitioning: A Case in Human Bone Simulations. Algorithmic and Statistical Perspectives on Large-Scale Data Analysis. Computational Challenges in Emerging Combinatorial Scientific Computing Applications. Spectral Graph Theory.

Algorithms for Visualizing Large Networks.

—John T. Saccoman, MAA Reviews, October 2012

“The book owes its textbook appeal to detailed proofs, a large number of fully elaborated examples and observations, and a handful of exercises, making beginning graduate students as well as advanced undergraduates its primary audience.

Still, it can serve as a useful reference book for experienced researchers as well.”

—Zentralblatt MATH

• Consolidates the important papers on Laplacian matrices into one succinct source • Illustrates how the properties of a matrix can provide information about the associated graph and vice versa • Includes enhanced proofs to reach a wider audience • Gives clear examples to illustrate each theorem and calculations • Contains several “excursion sections” and “application sections” that show interesting applications of the material

Selected Contents: Matrix Theory Preliminaries. Graph Theory Preliminaries. Introduction to Laplacian Matrices.

Algebraic Connectivity. The Fiedler Vector and Bottleneck Matrices for Trees. Bottleneck Matrices for Graphs. The Group Inverse of the Laplacian Matrix.

Catalog no. K12933, January 2012, 425 pp.

ISBN: 978-1-4398-6337-4, $93.95 / £59.99 Also available as an eBook

Catalog no. K11349, January 2012, 600 pp.

ISBN: 978-1-4398-2735-2, $93.95 / £59.99 Also available as an eBook

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

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Our Full Range of Titles RC4 Stream Cipher and Its Variants

Handbook of Product Graphs

Goutam Paul Subhamoy Maitra

Richard Hammack, Wilfried Imrich, and Sandi Klavžar

Second Edition

Indian Statistical Institute, Kolkata

“This remarkable monograph is ‘the first one on RC4.’ The theory surrounding the development of RC4 is very helpful for the study of stream ciphers in general, as the authors say. The book will be of interest to scholars and students whose expertise lies in cryptography, applied mathematics, computer security, and so on.”

—Zhixiong Chen, Mathematical Reviews, January 2013

“I am delighted to introduce the first complete book on RC4, the most popular and widely deployed software stream cipher. … This book contains not only the authors’ own research materials, but it has nicely assimilated the results of others to make it a complete treatise on RC4 and its variants. I believe this book will be widely accepted as an important research monograph by both the students and experienced researchers in the field of cryptology.”

—From the Foreword by Bimal Roy, Founder of the Cryptology Research Society of India and Director of the Indian Statistical Institute

• Represents the first complete book on RC4 • Requires no prior knowledge of cryptography • Introduces basic concepts, such as private/public key cryptosystems and block/stream ciphers, before covering advanced material • Elucidates the theoretical underpinnings and experimental observations • Includes end-of-chapter research problems that highlight opportunities for future research • Offers a comprehensive bibliography of RC4 literature

Selected Contents: Introduction to Cryptography. Stream Ciphers and RC4. Analysis of Key Scheduling. Key Recovery from State Information. Analysis of Keystream Generation.

Distinguishing Attacks. WEP and WPA Attacks. Fault Attacks. Variants of RC4. Stream Cipher HC-128.

Conclusion. Appendices. Bibliography. Index.

Catalog no. K11529, November 2011, 311 pp.

ISBN: 978-1-4398-3135-9, $98.95 / £62.99 Also available as an eBook

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“It is my pleasure to introduce you to the marvelous world of graph products, as presented by three experts in a hugely expanded and updated edition of the classic by Imrich and Klavžar.

This version, really a new book (33 chapters, up from nine!), contains streamlined proofs, new applications, solutions to conjectures (such as Vizing’s conjecture for chordal graphs), and new results in graph minors and flows. Every graph theorist, most combinatorialists, and many other mathematicians will want this volume in their collection. … The old book was already a delight, and you will want the new one in an accessible place on your bookshelf.”

—From the Foreword by Peter Winkler, Dartmouth College

• Offers a thorough introduction to the Cartesian, strong, direct, and lexicographic products and their subgraphs • Presents numerous results and algorithms, including some that solve long-standing questions • Illustrates applications of graph products in several areas, including dynamic location theory, chemistry, human genetics, structural mechanics, and graph visualization • Describes the dot product, the random dot product, and applications to the generation of random graphs with prescribed properties • Applies the free product of graphs to infinite median graphs • Defines the zig-zag and replacement products • Contains well over 300 exercises, with hints or full solutions in the appendix • Provides sample implementations of selected algorithms and other useful information on the book’s website

Selected Contents: A Brief Introduction to Graphs and Their Products.

Factorization and Cancellation. Isometric Embeddings. Algorithms. Invariants. Related Concepts. Appendix. Bibliography. Indices.

Catalog no. K10662, June 2011, 536 pp.

ISBN: 978-1-4398-1304-1, $109.95 / £69.99 Also available as an eBook

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Our Full Range of Titles Bijective Combinatorics Nicholas Loehr Virginia Polytechnic Institute and State University, Blacksburg, USA

“This textbook, aimed at beginning graduate students, is the first to survey the subject emphasizing the role of bijections. … The exposition is careful and deliberate, and leaves no stone unturned … a welcome addition to the literature and a very nice book.”

—David Callan, Mathematical Reviews, 2012

“I found this book engaging. The proofs are very clear, and in many cases several proofs are offered. … This book could serve several purposes. By focusing on the first half of the book, it could be an excellent choice for a first course in combinatorics for senior undergraduates. By selecting topics and/or moving quickly, it could work well for a more mature audience. … it also makes a great reference for people who use combinatorics but are not specialists. …

This is a very nice book that deserves serious consideration.”

—Peter Rabinovitch, MAA Reviews, September 2011

• Emphasizes bijective methods and combinatorial proofs • Requires minimal mathematical prerequisites • Includes a careful treatment of ranking, unranking, and successor algorithms • Provides detailed coverage of algebraic topics, such as formal power series, group actions, and symmetric polynomials, from a combinatorial viewpoint • Contains numerous worked examples and applications as well as nearly 1,000 exercises, ranging in difficulty from routine verifications to unsolved problems • Offers solutions, hints, or partial answers to many of the exercises at the end of the book

Selected Contents: Introduction. Basic Counting. Combinatorial Identities and Recursions. Counting Problems in Graph Theory. Inclusion-Exclusion and Related Techniques. Ranking and Unranking. Counting Weighted Objects. Formal Power Series. The Combinatorics of Formal Power Series. Permutations and Group Actions. Tableaux and Symmetric Polynomials. Abaci and Antisymmetric Polynomials.

Additional Topics. Answers and Hints to Selected Exercises. Bibliography. Index.

Catalog no. K12206, February 2011, 612 pp.

ISBN: 978-1-4398-4884-5, $109.95 / £69.99

Discrete Structures with Contemporary Applications Alexander Stanoyevitch California State University–Dominguez Hills, Carson, USA

“… this is the most physically readable textbook that I have seen in a long time. … there are many examples and in many cases proofs of the theorems are included. A large number of exercises are provided and split into two categories, the traditional math problem and exercises to be performed on a computer. … The two most important courses in the computer science major are the first programming and discrete math classes.

Each establishes a foundation of skills that will be repeatedly used throughout the major field of study and this book is an excellent text for the development of the needed skills in math.”

—Charles Ashbacher, MAA Reviews, March 2011

• Covers many applications of discrete mathematics, including simulations, genetic algorithms, network flows, probabilistic primality tests, public key cryptography, and coding theory • Presents algorithms in pseudo code • Offers sample programs via the author’s website • Illustrates difficult concepts with over 300 figures • Follows the recommendations of the ACM • Introduces several supplementary topics that can form an excellent basis for student projects • Includes a wide variety of examples and exercises, with solutions in the appendices • Incorporates computer exercises that teach students how to write their own programs

Selected Contents: Logic and Sets. Relations and Functions, Boolean Algebra, and Circuit Design. The Integers, Induction, and Recursion. Number Systems. Counting Techniques, Combinatorics, and Generating Functions. Discrete Probability and Simulation.

Complexity of Algorithms. Graphs, Trees, and Associated Algorithms. Graph Traversal and Optimization Problems. Randomized Search and Optimization Algorithms. Appendices. References.

Index.

Catalog no. K10918, January 2011, 1002 pp.

ISBN: 978-1-4398-1768-1, $104.95 / £46.99 Also available as an eBook

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CALL FOR AUTHORS Aims and Scope The Discrete Mathematics and Its Applications series publishes professional reference works and upper-division undergraduate and graduate textbooks. The series seeks to publish books that provide systematic and detailed treatments of areas that have gone through significant progress in recent years and whose progress is served by translation into full-length books. We encourage experts of such areas to contact us and increase the visibility of their specialty by authoring books for the series.

Series Editors Miklos Bona Professor, University of Florida

bona@ufl.edu Ph: (352) 392-0281 Fax: (352) 392-8357

Donald Kreher Professor, Michigan Technological University

kreher@mtu.edu Ph: (906) 487-3542 Fax: (906) 487-3133 Proposals for the series may be submitted to one of the series editors or directly to:

Robert E. Ross Senior Editor

CRC Press Mathematics robert.ross@taylorandfrancis.com Ph: (978) 358-7668 Cell: (781) 535-9277