Counting Rocks! An Introduction to Combinatorics

Format:

Book

Author/Creator:

Adams, Henry, author.

Emmrich, Kelly, author.

Gillespie, Maria, author.

Golden, Shannon, author.

Pries, Rachel, 1972- author.

Language:

English

Subjects (All):

Mathematics--Textbooks.

Mathematics.

Physical Description:

1 online resource

Place of Publication:

[Place of publication not identified] Henry Adams, Rachel Pries, and Maria Gillespie 2023.

Language Note:

In English.

Summary:

This textbook, Counting Rocks!, is the written component of an interactive introduction to combinatorics at the undergradaute level. Throughout the text, we link to videos where we describe the material and provide examples; see the Youtube playlist on the Colorado State University (CSU) Mathematics YouTube channel. 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 graph theory (Chapters 8-12). The material and the problems we include are standard for an undergraduate combinatorics course. In this text, one of our goals was to describe the mathematical structures underlying problems in combinatorics. For example, we separate the description of sequences, permutations, sets and multisets in Chapter 3. In addition to the videos, we would like to highlight some other features of this book. 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 online computing software SAGE in order to solve problems; this is especially useful for the problems on recurrence relations. We have included many helpful figures throughout the text, and we end each chapter (and many of the sections) with a list of exercises of varying difficulty.

Contents:

Preface

Contents

What is combinatorics?

Counting principles

Counting combinations

Pascal's triangle and the Binomial Theorem

Proof techniques in combinatorics

Recurrence relations

Generating functions

Graph theory basics

Trees

Graph optimization

Planar graphs

Graph coloring

Notes:

Description based on online resource