Counting Rocks! An Introduction to Combinatorics

TL;DR

"Counting Rocks!" is an undergraduate textbook introducing combinatorics through interactive content, videos, and software tools, covering counting, proof techniques, recurrence relations, generating functions, and graph theory.

Contribution

It provides an accessible, multimedia-rich introduction to combinatorics with integrated software tools and investigation sections for deeper understanding.

Findings

Includes standard undergraduate topics in combinatorics

Uses videos and SAGE software for interactive learning

Contains exercises and illustrative figures

Abstract

This textbook, "Counting Rocks!", is the written component of an interactive introduction to combinatorics at the undergraduate level. Throughout the text, we link to videos where we describe the material and provide examples. The major topics in this text are counting problems (Chapters 1-4), proof techniques (Chapter 5), recurrence relations and generating functions (Chapters 6-7), and an introduction to graph theory (Chapters 8-12). The material and the problems we include are standard for an undergraduate combinatorics course. In addition to the linked videos, most chapters contain an investigation section, where students are led through a series of deeper problems on a topic. In several sections, we show students how to use the free, open source computing software SAGE in order to solve problems. We have included many illustrative figures throughout the text, and we end each section and chapter with a list of exercises of varying difficulty.