Edited by Maria Cristina Pedicchio, Walter Tholen

The book gives a categorical introduction to some of the key areas of modern mathematics. Researchers, teachers and graduate students in algebra and topology familiar with the very basic notions of category theory will find all the advanced tools needed for their subjects, without being forced to study category theory for its own sake. Rather, each of the eight largely independent chapters takes the reader on a journey through a particular subject, showing the power and applicability of the categorical foundations in each case.

R. A. Bailey

Association schemes are of interest to both mathematicians and statisticians and this book is written with both audiences in mind. It has arisen from a course successfully taught by the author and as such the material is thoroughly class-tested. There are numerous examples and exercises that will increase the book's appeal to both graduate students and their instructors. It is ideal for those coming either from pure mathematics or statistics backgrounds wishing to bring their understanding of association schemes up to the state of the art.

Josef Lauri, Raffaele Scapellato

The aim of this book is to provide in-depth coverage of selected areas of graph theory, with a focus on symmetry properties of graphs. As much as possible, the authors have tried to present results and proofs which are not often to be found in textbooks. Any student who has mastered the contents of this book will be well prepared for current research in many aspects of the theory of graph automorphisms and the reconstruction problem.

Peter J. Cameron

This is a combinatorics textbook aimed at second-year undergraduates to beginning graduates, stressing common techniques (such as generating functions and recursive construction) which underlie the great variety of subject matter. The book is divided into two parts, the second at a higher level and with a wider range than the first. Historical notes give a wider perspective on the subject. More advanced topics are given as projects, and there are a number of exercises, some with solutions given.

Richard P. Stanley, Appendix by Sergey Fomin

This is the second volume of a two-volume work on enumerative combinatorics, an area of mathematics with connections to many other fields, such as computer science, spectroscopy, algebraic geometry, algebraic topology, and representation theory. Many topics covered (notably, the theory of symmetric functions) are not available in any other textbook at this level, and the book's usefulness is enhanced by over 250 exercises with solutions. Although primarily a graduate student textbook and a resource for professional mathematicians, some parts will be accessible to mathematics undergraduates and even interested amateurs.

Richard P. Stanley, Foreword by Gian-Carlo Rota

Enumerative combinatorics deals with the basic problem of counting how many objects have a given property. Since this problem arises in many areas of mathematics and science the subject is of great applicability. This book provides an introduction to the subject at a level suitable for graduate students and research mathematicians.

Tom Leinster

Higher-dimensional category theory draws its inspiration from areas as diverse as topology, quantum algebra, mathematical physics, logic, and theoretical computer science. The heart of this book is the language of generalized operads. This is a natural and transparent language for higher category theory which the author introduces carefully and methodically. This is the first book on the subject and lays its foundations. It will appeal to both graduate students and established researchers who wish to become acquainted with this modern branch of mathematics.

Thomas Forster

This is an introduction to logic and the axiomatization of set theory from a unique standpoint. Philosophical considerations are given careful consideration, and the author places the notion of inductively defined sets (recursive datatypes) at the centre of his exposition. The presentation is engaging, but always great care is taken to illustrate difficult points. Understanding is also aided by the inclusion of many exercises. Little previous knowledge of logic is required of the reader, and only a background of standard undergraduate mathematics is assumed.

Edited by Richard J. Nowakowski

Is Nine-Men Morris, in the hands of perfect players, a win for white or for black - or a draw? Can king, rook, and knight always defeat king and two knights in chess? What are nimbers, tinies, switches, minies? This book deals with combinatorial games, that is, games not involving chance or hidden information. The first part of the book will be accessible to anyone, regardless of background: it contains introductory expositions, reports of unusual tournaments, and a fascinating article by John H. Conway on the possibly everlasting contest between an angel and a devil. For those who want to delve more deeply, the book also contains combinatorial studies of chess and Go, plus reports on computer advances and new theoretical approaches. If you have read and enjoyed Martin Gardner, or if you like to learn and analyze new games, this book is for you.

Edited by Richard J. Nowakowski

This fascinating collection of articles by some of the top names in the field is a state-of-the-art look at combinatorial games. The articles run the gamut from new theoretical approaches, where computer science now plays as much of a role as mathematics, to the very latest in some of the hottest games, such as Amazons, Chomp, Dot-and-Boxes, Go, Chess, Hex. Most articles give information helpful in playing or analyzing the games, and some go so far as to give explicit strategies for solving them. This volume, like its predecessor, Games of No Chance, should be on the shelf of all serious combinatorial games enthusiasts.

J. F. Humphreys, M. Y. Prest

This textbook is an introduction to algebra via examples and will appeal to computer science as well as mathematics students. This second edition contains new material on mathematical reasoning skills and a new chapter on polynomials. The book was developed from first-level courses taught in the UK and USA and can be used at a wide range of levels: for first- or second-level university students, and also as enrichment material for upper-level school students. Throughout the book the authors pay attention to the historical development of mathematical ideas.

Krzysztof Ciesielski

This text presents methods of modern set theory as tools that can be usefully applied to other areas of mathematics, such as abstract geometry, real analysis, and, in some cases, topology and algebra. These methods include transfinite induction, Zorn's Lemma, the Continuum Hypothesis, Martin's Axiom, the Diamond Principle and elements of forcing. Written primarily as a text for beginning graduate or advanced level undergraduate students, this book should also interest researchers wanting to learn more about set theoretical techniques applicable to their fields.

F. William Lawvere, Robert Rosebrugh

Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. For the first time in a text, this book uses categorical algebra to build such a foundation, starting from intuitive descriptions of mathematically and physically common phenomena and advancing to a precise specification of the nature of Categories of Sets. An Appendix provides an explicit introduction to necessary concepts from logic, and an extensive Glossary provides a window to the mathematical landscape.

Dragoš Cvetkovic, Peter Rowlinson, Slobodan Simic

Line graphs have the property that their least eigenvalue is greater than or equal to -2, a property shared by generalized line graphs and a finite number of so-called exceptional graphs. This book deals with all these families of graphs in the context of their spectral properties. The authors discuss the three principal techniques that have been employed, namely 'forbidden subgraphs', 'root systems' and 'star complements'. They bring together the major results in the area, including the recent construction of all the maximal exceptional graphs. Technical descriptions of these graphs are included in the appendices, while the bibliography provides over 250 references. This will be an important resource for all researchers with an interest in algebraic graph theory.

Krzysztof Ciesielski, Janusz Pawlikowski

This book explores a new axiom of set theory, CPA, the Covering Property Axiom. CPA is consistent with the usual ZFC axioms, indeed it is true in the iterated Sacks model and actually captures the combinatorial core of this model. A plethora of results known to be true in the Sacks model easily follow from CPA. Replacing iterated forcing arguments with deductions from CPA simplifies proofs, provides deeper insight, and leads to new results. Researchers who use set theory in their work will find much of interest in this book.

Martin Charles Golumbic, Ann N. Trenk

Algorithmic graph theory finds numerous applications, from data transmission through networks to efficiently scheduling aircraft. An important branch of this theory is tolerance graphs and tolerance orders which receive their first rigorous treatment in book form here. This book contains proofs of major results that were previously scattered throughout the literature and it will act as a springboard for researchers, especially graduate students, to pursue new directions of investigation. With many examples and exercises it is also suitable for use as the text for a graduate course in graph theory.