Combinatorics Through Guided Discovery

Kenneth P. Bogart

Digital versions PDF and HTML
PreTeXt source Yes
Exercises Yes
Solutions Solution manual available to instructors
License GNU Free Documentation License

As the title suggests this book is designed for a “discovery method” course. The heart of the book is the hundreds of exercises that guide the student through the key ideas of enumerative combainatorics and a brief introduction to graph theory. The exercises are marked with special symbols to indicate their role in the course, for example, whether they are essential or motivational. The chapter titles are

  1. What is Combinatorics?
  2. Applications of Induction and Recursion in Combinatorics and Graphy Theory
  3. Distribution Problems
  4. Generating Functions
  5. The Principle of Inclusion and Exclusion
  6. Groups Acting on Sets

The three supplmental sections deal with relations, mathematical induction, and exponential generating functions.

This book is the result of an NSF project led by Ken Bogart and is currently maintained by the Mathematics Department of Dartmouth College.