01 / Reading Guide
Reading Guide
Who this book is for
For undergraduates taking a second discrete mathematics or combinatorics course, especially in computing and applied mathematics. The examples develop the habit of choosing a representation before calculating. Readers should be ready to write explanations and proofs, rather than treat counting formulas as isolated recipes to memorize.
Prerequisites
An initial discrete mathematics course and mathematical induction are recommended. Review sets, functions, binomial coefficients, graph notation and elementary algebra; probability and generating-function techniques develop within the course.
What it covers
Enumeration, induction, graphs, partially ordered sets, inclusion-exclusion, generating functions, recurrence equations and probability connect with graph algorithms and network flows. Further applications show how related techniques solve different-looking problems. The book’s course history and author commentary explain its emphasis on practical mathematical reasoning alongside formal development.
How to use it
For a counting problem, define exactly what constitutes one object and decide whether order or repetition matters. Solve a small case by explicit enumeration before applying a general formula. Draw a graph or poset when relations matter more than arithmetic. Compare a recurrence with a generating-function solution and verify that they produce the same initial terms. For optimization, check the model’s constraints before interpreting the result. Write down a failed attempt and the structural clue that suggested a better approach.
Edition and sources
The authors’ complete archived 2016 edition remains readable as a stable full book under CC BY-SA 4.0. Newer revisions are maintained separately. Use the archived edition consistently when comparing chapter references, exercises or notation with a course syllabus.
