Applied Combinatorics

Recommended by one of my professors. Fairly clear and useful when I need to clarify something gone over in class.

We used this text for our introductory class in Combinatorics in graduate Mathematics at Louisville. Very well written with fantastic examples.

Simply stated, this is an excellent book. I used this book to teach an upper division undergraduate course in Graph Theory and Combinatorics. This book is by far the best book I have come across for teaching these topics. Incredibly the book contains very few errors (I've only found two errors (typos) ). In addition, the book has applications of the concepts for a wide range of disciplines.The author has a wide range of problems at the end of each section. Almost all of the problems are well written with clear directions. Every Computer Science/Mathematics major should have this book in their library. It's great!

I really enjoyed this book. I am a mathematics major and am currently in my senior year. This book helped me earn an 'A' in my upper division combinatorics course. My fellow classmate said that he hated this book and he refused to read it; he was very sorry when the end of quarter grades were posted. I developed a love for combinatorics from this book and I went on to take an advanced combinatorics class which used this same book. I found it to be satisfying there to!

This book offers a good mix of both theory and practice. Roberts does writes well the proofs, but doesn't get lost in the stratosphere of theory, instead coming down to Earth with a huge collection of applications. It has many good chapters in enumerative combinatorics, which are well written and offers an array of applications. These chapters teach how to count in a friendly way, and the students should enjoy them. For example, the topic on counting with repeated elements is very enjoyable. The chapter on Polya's Theory, which is a difficult subject is presented in a very ``user-friendly'' approach with intermediate applications, that allow the reader to understand more thoroughly the subject. This is just one of many examples of the good writing skills of Roberts. It also has several chapters on graph theory, with an even greater emphasis on its applications. These chapters deal with the subject both from a mathematician point of view, with interesting theorems, and from the point of view of the computer scientist, with several graph algortihms. The chapter on networks and the Ford-Fulkerson algorithm and its applications is very well written. Also very good is the chapter on codes. Unfortunately it ties the Hadamard codes with a previous chapter on designs, when it can be covered with slight alterations independently. Another good interesting feature of the book is the bibliography, which invites further exploration of the topics. The exercises both complement the theory and show how it is applied. Furthermore, there are many examples of applications which ``continue'' from one chapter to another, exploring them from many different points of view. In general this is an extremely recommendable book for those interested either in how to count things, and also in those interested in Computer Science. I have used for two different (introductory) courses (one of each kind) with high success in both cases. (Although in the course in Computer Science I had to complement the book with others). In short, if you have to teach an introductory course in either enumerative combinatorics, graph theory and/or graph algorithms this may be your book. The only drawback is perhaps the time elapsed since published. I wonder whether there is a new edition. If there is not, there should be. Roberts' style is magnificent.