Combinatorics: A Guided Tour is an undergraduate textbook designed for a first course or reading course in combinatorics. A student learning from this book should have taken one year of calculus and an introduction to proofs. The book takes a more theoretical approach in presenting combinatorics, in contrast to some of the more application-based combinatorics books on the market.
The book is written in an informal and somewhat wordy style. It has a bit of personality and makes for an enjoyable read. It would be a suitable book for students to attempt to read on their own and then discuss in a classroom setting.
The author uses two different types of questions throughout the book: exercises and reading questions. The exercises are given at the end of each section. They are numerous and well written. Hints and answers to selected exercises are given in the back of the book. The reading questions are scattered throughout the text and are a great feature. They are designed to be answered while reading and could be assigned to students to complete before discussing the topic in class.
When combinatorial proofs are given, the author provides a question regarding the number of items in a particular set and gives two appropriate counting methods. It appears to be a very clear way of explaining what can be a difficult concept for students new to the subject to grasp.
Overall, I believe the author succeeded writing a book that would be understandable, readable and enjoyable for undergraduates.
Michael Rowell is an Assistant Professor of Mathematics at Pacific University. His research interests are in Combinatorics and Number Theory. His website is www.math.pacificu.edu/~rowell and his email is email@example.com.