The subtitle accurately specifies in which category of textbooks this book belongs: introductory textbooks for a Discrete Mathematics course. There are many competing textbooks in that group, with almost completely matching sets of topics covered. Therefore, the task of the reviewer is to describe what distinguished the book at hand from competing textbooks, and where the book at hand sits on the scale of available choices.
This reviewer believes that this textbook is on the more advanced, more challenging side. Most topics are developed further than in competing textbooks. This is true for almost every chapter. One exception is Chapter 3 (Sets, Combinatorics, Probability and Number Theory), where even this, otherwise courageous, author does not dare to make the brave step of covering generating functions. When recurrence relations are discussed without explaining generating functions, this reviewer always gets the feeling that readers are told a very funny and entertaining joke, but the punchline is not revealed to them.
Though the topical coverage is ambitious, the exercises are less so. There are plenty of easy and moderately difficult exercises, but it is hard to find any that will be really challenging for good students. On the other hand, the coverage of applications is more thorough than in competing textbooks. For this reason, this reviewer thinks that this book is the right choice for your class if you have good students, but most of them plan to take a job after their get their undergraduate degree instead of going to graduate school.
Miklós Bóna is Professor of Mathematics at the University of Florida.