• Improved Introduction and Organization--For the sixth edition the first part of the book has been restructured to present core topics in a more efficient, more effective, and more flexible way.
Coverage of mathematical reasoning and proof is concentrated in the first chapter, and the process of making conjectures and using different proof methods and strategies to tackle them is now illustrated using easily-accessible topics such as tilings of checkerboards. Introductory material on discrete structures has been separated into its own chapter, induction and recursion coverage is now exclusively focused in a single chapter, and coverage of number theory is now more flexible with optional material separated into different sections.
• Expanded and Improved Coverage--The sixth edition offers brand-new or expanded coverage in several key areas to present important topics with better care, detail, and flexibility.
Logic topics such as conditional statements and De Morgan's laws receive expanded coverage, and truth tables are introduced earlier and in more detail. A brand new section on Bayes' Theorem is provided, with useful applications for constructing spam filters. Mathematical induction coverage has been enhanced, providing better motivation and examples. Coverage of counting techniques has been expanded, with new coverage on the ways in which objects can be distributed in boxes. The introduction to graph theory has been streamlined and improved, with quicker introduction to terminology and greater emphasis on making correct decisions when building graph models. And a new Appendix has been added showing basic axioms for real numbers and integers.
• Exercises – There are over 3800 exercises in the text, from straightforward problems that develop basic skills to a large number of intermediate and challenging exercises. Exercise sets also contain special discussions that develop new concepts not covered in the text, enabling students to discover new ideas through their own work. Each chapter is followed by a rich and varied set of Supplementary Exercises that reinforce the concepts of the chapter and integrate different topics more effectively, and a set of Writing Projects designed to tie together mathematical concepts and the writing process to expose students to possible areas for further study. For courses that utilize programming, sets of Computer Projects tie concepts in discrete math together what students may have learned about computing, and Computation and Exploration exercises allow students to uncover new facts and ideas about discrete math using mathematical computation software such as Maple or Mathematica.
New for this edition--The sixth edition adds over 400 new exercises to this comprehensive mix, with more on key concepts, more introducing new concepts, and more challenging exercises. Extra effort has been made to ensure that both odd- and even-numbered exercises are provided for basic concepts.
• Worked Examples – Over 750 examples are used to illustrate concepts, relate different topics, and introduce applications.
New for this edition--The sixth edition adds many new routine examples, especially at spots where key concepts are introduced. A better correspondence has also been made between examples made introducing key concepts and routine exercises.
• Historical Information – The background of many topics are succinctly described in the text using historical footnotes and brief biographies of more than 65 mathematicians and computer scientists who were (and are) important contributors to discrete mathematics.
New for this Edition--New biographies have been added for Archimedes, Hopper, Stirling, and Bayes, and many biographies and historical notes from the previous edition have been updated and enhanced.