Counting Rocks! An Introduction to Combinatorics

Henry Adams, Kelly Emmrich, Maria Gillespie, Shannon Golden, and Rachel Pries

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  • Text for a first course in combinatorics
  • Latest version: January 2023
  • 224 pages, 12 chapters
  • Accompanied by 47 videos, 15 minutes average length, covering entire course
  • For more information and to download

This textbook is one half of an interactive course from Colorado State University. The other half of the course consists of 47 videos that are also freely available on the CSU YouTube channel. The text has convenient links to the videos so that it is easy to find the video matching the topic. The text and videos have now been used for a number of years in their one-semester introductory combinatorics course that also includes some graph theory. It can also reasonably be used in a strictly combinatorics course on a quarter calendar by covering chapters 1-7.

Most chapters contain an investigative section that goes more deeply into a topic. There are several examples throughout the book that use Sage with the twin goals of introducing Sage and of solving problems that are impractical to do by hand.

Table of Contents

  1. What is Combinatorics?
  2. Counting Principles
  3. Counting Combinations
  4. Pascal’s Triangle and the Binomial Theorem
  5. Proof Techniques in Combinatorics
  6. Recurrence Relations
  7. Generating Functions
  8. Graph Theory Basics
  9. Trees
  10. Graph Optimization
  11. Planar Graphs
  12. Graph Coloring