离散与组合数学手册：第二版（上下）英文

The purpose of the Handbook of Discrete and Combinatorial Mathematics is to provide a comprehensive reference volume for computer scientists， engineers， mathematicians，as well as students， physical and social scientists， and reference librarians， who need information about discrete and combinatorial mathematics：This first edition of this book was the first resource that presented such information in a ready-reference form designed for all those who use aspects of this subject in their work or studies. This second edition is a major revision of the first edition. It includes extensive additions and updates， summarized later in this preface. The scope of this handbook includes the many areas generally considered to be parts of discrete mathe-matics， focusing on the information considered essential to its application in computer science， engineering， and other disciplines.

The importance of discrete and combinatorial mathematics has increased dramatically within the last few decades. This second edition has been written to update all content and to broaden the coverage. We have been gratified by the success of the first edition of the Handbook. We hope that the many readers who have asked for a second edition will find it worth the wait.The purpose of the Handbook of Discrete and Combinatorial Mathematics is to provide a comprehensive reference volume for computer scientists， engineers， mathematicians，as well as students， physical and social scientists， and reference librarians， who need information about discrete and combinatorial mathematics：This first edition of this book was the first resource that presented such information in a ready-reference form designed for all those who use aspects of this subject in their work or studies. This second edition is a major revision of the first edition. It includes extensive additions and updates， summarized later in this preface. The scope of this handbook includes the many areas generally considered to be parts of discrete mathe-matics， focusing on the information considered essential to its application in computer science， engineering， and other disciplines. Some of the fundamental topic areas covered
　　in this edition include：
　　logic and set theory
　　enumera.tion
　　integer sequences
　　recurrence relations
　　generating functions
　　number theory
　　abstract algebra
　　linear algebra
　　discrete probability theory
　　data mining
　　discrete bioinformatics
　　graph theory
　　trees
　　network flows
　　combinatorial designs
　　computa，tional geometry
　　coding theory
　　cryptography
　　discrete optimization
　　automata theory
　　data structures and algorithms
　　Format
　　The material in the Handbook is presented so that key information can be located and used quickly and ea.sily. Each chapter includes a glossary that provides succinct defini-tions of the most important terms from that chapter. Individual topics are covered in sections and sub. sections within chapters， each of which is organized into clearly identi-fiable parts： definitions， facts， and examples. Lists of facts include： information about how material is used and why it is important
　　historicalinformation
　　key theorems
　　the latest results
　　the status of open questions
　　tables of numerical values， generally not easily computed
　　summary tables
　　key algorithms in simple pseudocode
　　information about algorithms， such as their complexity
　　major applications
　　pointers to additional resources， both websites and printed material.
　　Facts are presented concisely and are listed so that they can be easily found and un-derstood. Cross-references linking portions of the Handbook are also provided. Readers who wish to study a topic further can consult the resources listed.The material in the Handbook has been chosen for inclusion primarily because it is important and useful. Additional material has been added to ensure comprehensiveness so that readers encountering new terminology and concepts from discrete mathematics in their explorations will be able to get help from this book.Examples are provided to illustrate some of the key definitions， facts， and algorithms.
　　Some curious and entertaining facts and puzzles that some readers may find intriguing are
　　also included. Readers will also find an extensive collection of biographies after the main chapters， highlighting the lives of many important contributors to discrete mathematics.Each chapter of the book includes a list of references divided into a list of printed resources and a list of relevant websites.
　　How This Book Was Developed The organization and structure of the first edition of this Handbook were developed by a team that included the chief editor， three associate editors， a project editor， and the editor from CRC Press. This team put together a proposed table of contents which was then analyzed by members of a group of advisory editors， each an expert in one or more aspects of discrete mathematics. These advisory editors suggested changes，including the coverage of additional important topics. Once the table of contents was fully developed， the individual sections of the book were prepared by a group of more than 70 contributors from industry and academia who understand how this material is used and why it is important. Contributors worked under the direction of the associate editors and chief editor， with these editors ensuring consistency of style as well as clarity and comprehensiveness in the presentation of material. Material was carefully reviewed by authors and our team of editors to ensure accuracy and consistency of style.For the second edition， a new team was assembled. The first goal of this team was to put together a new table of contents. This involved identifying opportunities for new chapters and new sections to broaden the scope and appeal of the second edition. With
　　 the help of previous and new contributors， additional material was developed and existing material was updated and expanded， following the style and maintaining， or improving，the presentation in the first edition.