Dependencies among the Chapters

The chapters of this book are fairly independent after the first few. When we say that later chapters do depend on, say, Chapter 2, we mean they depend on the essential material in that Chapter, as discussed below in Dependencies within Chapters.

The Prologue is not required for anything else, but it is short and introduces the key themes, so we recommend it.

Chapter 0 (Preliminaries). Almost everything in later chapters depends on elementary knowledge of this material. Therefore, as noted in the Chapter Summaries, cover as much or as little of it as your students preparation requires, and cover it at the beginning of the course or just when it seems needed.

All subsequent chapters depend on Chapter 1 (algorithms) and Chapter 2 (induction). These two chapters can be taught in series or in parallel.

Chapter 3 (graphs) and Chapter 4 (counting) are very much the traditional guts of discrete mathematics. Although there is not a strong dependence of later chapters on Chapters 3 4, graphs are used as examples in many places and simple counting arguments show up repeatedly.

Difference equations, being recursive entities, appear throughout the book, so the systematic approaches to them discussed in Chapter 5 are well worth covering.

Chapter 6 (probability) and Chapter 7 (logic) are independent of each other, and make less persistent use of our key themes than most earlier chapters. Still, they resolve and clarify many points that have come up earlier.

The Epilogue