This book stresses the connection between, and the applications of, design theory to graphs and codes. Beginning with a brief introduction to design theory and the necessary background, the book also provides relevant topics for discussion from the theory of graphs and codes.

Although graph theory, design theory, and coding theory had their origins in various areas of applied mathematics, today they are to be found under the umbrella of discrete mathematics. Here the authors have considerably reworked and expanded their earlier successful books on graphs, codes and designs, into an invaluable textbook. They do not seek to consider each of these three topics individually, but rather to stress the many and varied connections between them. The discrete mathematics needed is developed in the text, making this book accessible to any student with a background of undergraduate algebra. Many exercises and useful hints are included througout, and a large number of references are given.

This volume contains nine invited papers that survey many areas of current research in combinatorics both on the theoretical and practical side. Several papers may be regarded as summarizing our present state of knowledge in a particular topic.

Discrete mathematics has now established its place in most undergraduate mathematics courses. This textbook provides a concise, readable and accessible introduction to a number of topics in this area, such as enumeration, graph theory, Latin squares and designs. It is aimed at second-year undergraduate mathematics students, and provides them with many of the basic techniques, ideas and results. It contains many worked examples, and each chapter ends with a large number of exercises, with hints or solutions provided for most of them. As well as including standard topics such as binomial coefficients, recurrence, the inclusion-exclusion principle, trees, Hamiltonian and Eulerian graphs, Latin squares and finite projective planes, the text also includes material on the ménage problem, magic squares, Catalan and Stirling numbers, and tournament schedules.

Graphdrawingaddressestheproblemofconstructingrepresentationsofabstract graphs, networks, and hypergraphs. The 6th Symposium on Graph Drawing (GD '98) was held August 13{15, 1998, atMcGillUniversity, Montr eal, Canada.ItimmediatelyfollowedtheTenth Canadian Conference on Computational Geometry (CCCG '98), held August 10{12 at McGill. The GD '98 conference attracted 100 paid registrants from academic and industrial institutions in thirteen countries. Roughly half the p- ticipantsalsoattendedCCCG'98.Asinthepast, interactionamongresearchers, practitioners, andstudents fromtheoreticalcomputer science, mathematics, and the application areas of graph drawing continued to be an important aspect of the graph drawing symposium. In response to the call for papers and system demonstrations, the program committee received 57 submissions, of which 10 were demos. Each submission was reviewed by at least 4 members of the program committee, and comments were returnedto the authors.Following extensive email discussions andmultiple rounds of voting, the program committee accepted 23 papers and 9 demos. GD '98 also held an unrefereed poster gallery. The poster gallery contained 16 posters, 14 of which have abstracts in this volume. The poster gallery served to encourageparticipationfromresearchersinrelatedareasandprovidedast- ulating environment for the breaks between the technical sessions. In keeping with the tradition of previous graph drawing conferences, GD '98 held a graph drawing contest. This contest, which is traditionally a conference highlight, servestomonitorandtochallengethestateoftheartingraphdrawing. A report on the 1998 contest appears in this volume.

Several geometric problems can be formulated in terms of the arrangement of a collection of curves in a plane, which has made this one of the most widely studied topics in computational geometry. This book, first published in 1991, presents a study of various problems related to arrangements of lines, segments, or curves in the plane. The first problem is a proof of almost tight bounds on the length of (n,s)-Davenport-Schinzel sequences, a technique for obtaining optimal bounds for numerous algorithmic problems. Then the intersection problem is treated. The final problem is improving the efficiency of partitioning algorithms, particularly those used to construct spanning trees with low stabbing numbers, a very versatile tool in solving geometric problems. A number of applications are also discussed. Researchers in computational and combinatorial geometry should find much to interest them in this book.

This book, suitable for graduate students and professional mathematicians alike, didactically introduces methodologies due to Furstenberg and others for attacking problems in chromatic and density Ramsey theory via recurrence in topological dynamics and ergodic theory, respectively. Many standard results are proved, including the classical theorems of van der Waerden, Hindman, and Szemer di. More importantly, the presentation strives to reflect the extent to which the field has been streamlined since breaking onto the scene around twenty years ago. Potential readers who were previously intrigued by the subject matter but found it daunting may want to give a second look.

The National Security Agency funded a conference on Coding theory, Cryp- tography, and Number Theory (nick-named Cryptoday) at the United States Naval Academy, on October 25-27, 1998. We were very fortunate to have been able to attract talented mathematicians and cryptographers to the meeting. Unfortunately, some people couldn't make it for either scheduling or funding reasons. Some of these have been invited to contribute a paper anyway. In addition, Prof. William Tutte and Frode Weierud have been kind enough to allow the inclusion of some very interesting unpublished papers of theirs. The papers basically fall into three catagories. Historical papers on cryp- tography done during World War II (Hatch, Hilton, Tutte, Ulfving, and Weierud), mathematical papers on more recent methods in cryptography (Cosgrave, Lomonoco, Wardlaw), and mathematical papers in coding theory (Gao, Joyner, Michael, Shokranian, Shokrollahi). A brief biography of the authors follows. - Peter Hilton is a Distinguished Professor of Mathematics Emeritus at the State University of New York at Binghamton. He worked from 1941 to 1945 in the British cryptanalytic headquarters at Bletchley Park. Profes- sor Hilton has done extensive research in algebraic topology and group theory. - William Tutte is a Distinguished Professor Emeritus and an Adjunct Pro- fessor in the Combinatorics and Optimization Department at the Univer- sity of Waterloo. He worked from 1941 to 1945 in the British cryptana- lytic headquarters at Bletchley Park. Professor Tutte has done extensive research in the field of combinatorics.

Schubert varieties and degeneracy loci have a long history in mathematics, starting from questions about loci of matrices with given ranks. These notes, from a summer school in Thurnau, aim to give an introduction to these topics, and to describe recent progress on these problems. There are interesting interactions with the algebra of symmetric functions and combinatorics, as well as the geometry of flag manifolds and intersection theory and algebraic geometry.

The explanation of the formal duality of Kerdock and Preparata codes is one of the outstanding results in the field of applied algebra in the last few years. This result is related to the discovery of large sets of quad riphase sequences over Z4 whose correlation properties are better than those of the best binary sequences. Moreover, the correlation properties of sequences are closely related to difference properties of certain sets in (cyclic) groups. It is the purpose of this book to illustrate the connection between these three topics. Most articles grew out of lectures given at the NATO Ad vanced Study Institute on "Difference sets, sequences and their correlation properties." This workshop took place in Bad Windsheim (Germany) in August 1998. The editors thank the NATO Scientific Affairs Division for the generous support of this workshop. Without this support, the present collection of articles would not have been realized."

Knowledge spaces offer a rigorous mathematical foundation for various practical systems of knowledge assessment. An example is offered by the ALEKS system (Assessment and LEarning in Knowledge Spaces), a software for the assessment of mathematical knowledge. From a mathematical standpoint, knowledge spaces generalize partially ordered sets. They are investigated both from a combinatorial and a stochastic viewpoint. The results are applied to real and simulated data. The book gives a systematic presentation of research and extends the results to new situations. It is of interest to mathematically oriented readers in education, computer science and combinatorics at research and graduate levels. The text contains numerous examples and exercises and an extensive bibliography.

The invited lectures given at the 12th British Combinatorial Conference are contained in this volume. The lectures survey many areas of current research activity in combinatorics and its applications, including graph theory, designs and probabilistic graphs. This book provides a valuable survey for the present status of knowledge in combinatorics for mathematicians, computer scientists and engineers and research workers in combinatorics.

This is a new in paperback second edition of the acclaimed first edition. The second edition includes a new chapter on a family of symmetric functions depending rationally on two parameters and also a chapter on zonal polynomials.

From reviews of the first edition:

'Despite the amount of material of such great potential interest to mathematicians...the theory of symmetric functions remains all but unknown to the persons it is most likely to benefit...Hopefully this beautifully written book will put an end to this state of affairs...I have no doubt that this book will become the definitive reference on symmetric functions and their applications.' Bulletin of the AMS

'...In addition to providing a self-contained and coherent account of well-known and classical work, there is a great deal which is original. The book is dotted with gems, both old and new...It is a substantial and valuable volume and will be regarded as the authoritative source which has been long awaited in this subject.' LMS book reviews

From reviews of the second edition:

'Evidently this second edition will be the source and reference book for symmetric functions in the next future.' Zentralblatt fuer Mathematik

The papers in this volume were selected for presentation at the Fourth Annual International Computing and Combinatorics Conference (COCOON'98), held on August 12-14, 1998, in Taipei. The topics cover most aspects of theoretical computer science and combinatorics related to computing. Submissions to the conference this year was only conducted electronically. Thanks to the excellent software developed by the system team of the Institute of Information Science, we were able to make virtually all communications through the World Wide Web. A total of 69 papers was submitted in time to be considered, of which 36 papers were accepted for presentation at the conference. In addition to these contributed papers, the conference also included four invited presentations by Christo Papadimitriou, Michael Fishcher, Fan Chung Graham and Rao Kosaraju. It is expected that most of the accepted papers will appear in a more complete form in scienti?c journals. Moreover, selected papers will appear in a special issue of Theoretical Computer Science. We thank all program committee members, their support sta? and referees for excellent work within demanding time constraints. We thank all authors who submitted papers for consideration. We are especially grateful to our colleagues who worked hard and o?ered widely di?ering talents to make the conference both possible and enjoyable. August 1998 Wen-Lian Hsu and Ming-Yang Kao Program Co-chairs COCOON'98 Organization COCOON'98 is organized by the Institute of Information Science, Academia Sinica, Taipei, Taiwan, ROC and in cooperation with Institute of Information and Computing Machinery (IICM), Taiwan, ROC.

This book constitutes the strictly refereed post-conference proceedings of the 5th International Symposium on Graph Drawing, GD'97, held in Rome, Italy, in September 1997. The 33 revised full papers and 10 systems demonstrations presented were selected from 80 submissions. The topics covered include planarity, crossing theory, three dimensional representations, orthogonal representations, clustering and labeling problems, packing problems, general methodologies, and systems and applications.

This book constitutes the strictly refereed post-conference proceedings of the International Symposium on Graph Drawing, GD'96, held in Berkeley, California, in September 1996.
The 24 revised full papers and the 8 systems demonstrations presented in the book were carefully selected from a total of 50 papers and 24 demos submitted. Also included is a summary of the annual graph drawing competition. Among the topics covered are planarity, upward and orthogonal drawing, heuristics, experimental results, and graph drawing systems.

This book constitutes the refereed proceedings of the Third Annual International Computing and Combinatorics Conference, COCOON'97, held in Shanghai, China, in August 1997.
The volume presents 53 revised full papers selected from a total of 106 submissions. The papers are organized in sections on parallel and distributed computing, computational geometry, complexity, computational biology, computability, cryptography and computational finance, graph algorithms, algorithms, rewriting and logic, algorithms and applications, automata languages and complexity, and mathematical programming and genetic algorithms.

This book constitutes the proceedings of the Second Annual International Conference on Computing and Combinatorics, COCOON '96, held in June 1996 in Hong Kong.
The 44 papers presented in the book in revised version were carefully selected from a total of 82 submissions. They describe state-of-the-art research results from various areas of theoretical computer science, combinatorics related to computing, and experimental analysis of algorithms; computational graph theory, computational geometry, and networking issues are particularly well-presented.

This book is a continuation of Theory of Matroids (also edited by Neil White), and again consists of a series of related surveys that have been contributed by authorities in the area. The volume begins with three chapters on coordinatisations, followed by one on matching theory. The next two deal with transversal and simplicial matroids. These are followed by studies of the important matroid invariants. The final chapter deals with matroids in combinatorial optimisation, a topic of much current interest. The whole volume has been carefully edited to ensure a uniform style and notation throughout, and to make a work that can be used as a reference or as an introductory textbook for graduate students or non-specialists.

This book offers a well-organized, easy-to-follow introduction to combinatorial theory, with examples, notes and exercises. ." . . a very good introduction to combinatorics. This book can warmly be recommended first of all to students interested in combinatorics." Publicationes Mathematicae Debrecen

Cryptology: Classical and Modern, Second Edition proficiently introduces readers to the fascinating field of cryptology. The book covers classical methods including substitution, transposition, Alberti, Vigenere, and Hill ciphers. It also includes coverage of the Enigma machine, Turing bombe, and Navajo code. Additionally, the book presents modern methods like RSA, ElGamal, and stream ciphers, as well as the Diffie-Hellman key exchange and Advanced Encryption Standard. When possible, the book details methods for breaking both classical and modern methods. The new edition expands upon the material from the first edition which was oriented for students in non-technical fields. At the same time, the second edition supplements this material with new content that serves students in more technical fields as well. Thus, the second edition can be fully utilized by both technical and non-technical students at all levels of study. The authors include a wealth of material for a one-semester cryptology course, and research exercises that can be used for supplemental projects. Hints and answers to selected exercises are found at the end of the book. Features: Requires no prior programming knowledge or background in college-level mathematics Illustrates the importance of cryptology in cultural and historical contexts, including the Enigma machine, Turing bombe, and Navajo code Gives straightforward explanations of the Advanced Encryption Standard, public-key ciphers, and message authentication Describes the implementation and cryptanalysis of classical ciphers, such as substitution, transposition, shift, affine, Alberti, Vigenere, and Hill

This textbook thoroughly outlines combinatorial algorithms for generation, enumeration, and search. Topics include backtracking and heuristic search methods applied to various combinatorial structures, such as:
· Combinations
· Permutations
· Graphs
· Designs
·
Many classical areas are covered as well as new research topics not included in most existing texts, such as:
· Group algorithms
· Graph isomorphism
· Hill-climbing
· Heuristic search algorithms
·
This work serves as an exceptional textbook for a modern course in combinatorial algorithms, providing a unified and focused collection of recent topics of interest in the area. The authors, synthesizing material that can only be found scattered through many different sources, introduce the most important combinatorial algorithmic techniques - thus creating an accessible, comprehensive text that students of mathematics, electrical engineering, and computer science can understand without needing a prior course on combinatorics.

The primary object of the lecture notes is to develop a treatment of association schemes analogous to that which has been so successful in the theory of finite groups. The main chapters are decomposition theory, representation theory, and the theory of generators. Tits buildings come into play when the theory of generators is developed. Here, the buildings play the role which, in group theory, is played by the Coxeter groups. - The text is intended for students as well as for researchers in algebra, in particular in algebraic combinatorics.

Combinatorics is a book whose main theme is the study of subsets of a finite set. It gives a thorough grounding in the theories of set systems and hypergraphs, while providing an introduction to matroids, designs, combinatorial probability and Ramsey theory for infinite sets. The gems of the theory are emphasized: beautiful results with elegant proofs. The book developed from a course at Louisiana State University and combines a careful presentation with the informal style of those lectures. It should be an ideal text for senior undergraduates and beginning graduates.

Discrete Mathematics for Computer Science: An Example-Based Introduction is intended for a first- or second-year discrete mathematics course for computer science majors. It covers many important mathematical topics essential for future computer science majors, such as algorithms, number representations, logic, set theory, Boolean algebra, functions, combinatorics, algorithmic complexity, graphs, and trees. Features Designed to be especially useful for courses at the community-college level Ideal as a first- or second-year textbook for computer science majors, or as a general introduction to discrete mathematics Written to be accessible to those with a limited mathematics background, and to aid with the transition to abstract thinking Filled with over 200 worked examples, boxed for easy reference, and over 200 practice problems with answers Contains approximately 40 simple algorithms to aid students in becoming proficient with algorithm control structures and pseudocode Includes an appendix on basic circuit design which provides a real-world motivational example for computer science majors by drawing on multiple topics covered in the book to design a circuit that adds two eight-digit binary numbers Jon Pierre Fortney graduated from the University of Pennsylvania in 1996 with a BA in Mathematics and Actuarial Science and a BSE in Chemical Engineering. Prior to returning to graduate school, he worked as both an environmental engineer and as an actuarial analyst. He graduated from Arizona State University in 2008 with a PhD in Mathematics, specializing in Geometric Mechanics. Since 2012, he has worked at Zayed University in Dubai. This is his second mathematics textbook.