AIM logo

AIM Open Textbook Initiative

 
Main AIM
textbook
page		 Approved Textbooks
     Open source math textbooks
     for undergraduate courses		 Evaluation criteria
     What the Editorial Board looks for
     in evaluating books 		Editorial Board
     Brief profiles of the
     board members
 

The following book has met the evaluation criteria developed by the AIM Editorial Board.

Combinatorics Through Guided Discovery
  Kenneth P. Bogart

Digital versions pdf
Latex source No
Exercises Yes
Solutions Solution manual available to instructors
License Gnu Free Documentation License

  • Text for a first course in combinatorics
  • Copyright 2004 by author
  • 200 pages, 6 chapters, 3 supplemental sections
  • Over 400 exercises, many with links to online hints
  • Print version not availble but can be freely reproduced and distributed
  • For more information and to download

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 combinatorics 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