*(English)*Zbl 1044.00002

From the preface: The material in the handbook is presented so that key information can be located and used quickly and easily. Each chapter includes a glossary that provides succinct definitions of the most important terms from that chapter. Individual topics are covered in sections and subsections within chapters, each of which is organized into clearly identifiable parts: definitions, facts, and examples. The definitions included are carefully crafted to help readers quickly grasp new concepts. Important notation is also highlighted in the definitions. Lists of facts include: information about how material is used and why it is important; historical information; key theorems; the latest results; the status of open questions; tables of numerical values, generally not easily computed; summary tables; key algorithms in an easily understood pseudocode; information about algorithms, such as their complexity; major applications; pointers to additional resources, including websites and printed material. Facts are presented concisely and are listed so that they can be easily found and understood. Extensive crossreferences linking parts of the handbook are also provided. Readers who want 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.

Each chapter of the book includes a list of references divided into a list of printed resources and a list of relevant websites.

Contents: Jerrold W. Grossman, John G. Michaels, Susanna S. Epp, David Riley and Mukesh Dalal, Foundations (1–80); John G. Michaels, Jay Yellen, Edward W. Packel, Robert G. Rieper, George E. Andrews, Alan C. Tucker, Edward A. Bender and Bruce E. Sagan, Counting methods (81–134); Thomas A. Dowling, Ralph P. Grimaldi, Jay Yellen, Victor S. Miller, Edward A. Bender and Kenneth H. Rosen, Sequences (135–212); Kenneth H. Rosen, Jon Grantham, Carl Pomerance, Bart Goddard and Jeff Shallit, Number theory (213–298); John G. Michaels, Algebraic structures (299–354); Joel V. Brawley, Peter R. Turner, Barry Peyton, Esmond Ng and R. B. Bapat, Linear algebra (355–426); Joseph R. Barr, Peter R. Turner, Patrick Jaillet, Douglas R. Shier, Vidyadhar G. Kulkarni and Lawrence M. Leemis, Discrete probability (427–494); Lowell W. Beineke, Jonathan L. Gross, Stephen B. Maurer, Edward R. Scheinerman, Bennet Manvel, Arthur T. White, Paul K. Stockmeyer, Michael Doob, Stefan A. Burr and Andreas Gyarfas, Graph theory (495–602); Lisa Carbone, Uri Peled and Paul Stockmeyer, Trees (603–628); J. B. Orlin, Ravindra K. Ahuja, Douglas R. Shier, David Simchi-Levi, Sunil Chopra, Bruce L. Golden and B. K. Kaku, Networks and flows (629–716); Graham Brightwell and Douglas B. West, Partially ordered sets (717–752); Charles J. Colbourn, Jeffrey H. Dinitz and James G. Oxley, Combinatorial designs (753–796); Ileana Streinu, Karoly Bezdek, János Pach, Tamal K. Dey, Jianer Chen, Dina Kravets, Nancy M. Amato and W. Randolph Franklin, Discrete and computational geometry (797–888); Alfred J. Menezes and Paul C. van Oorschot, Coding theory and cryptology (889–954); Beth Novick, S. Louis Hakimi, Sunil Chopra, David Simchi-Levi, S. E. Elmaghraby, Michael Mesterton-Gibbons and Joseph R. Barr, Discrete optimization (955–1038); Jonathan L. Gross, William Gasarch, Aarto Salomaa, Thomas Cormen, Lane Hemaspaandra and Milena Mihail, Theoretical computer science (1039–1099); Charles H. Goldberg, Jonathan L. Gross, Jianer Chen, Viera Krnanova Proulx, Joan Feigenbaum and Sampath Kannan, Information structures (1101–1151).