Discrete Mathematics with Graph Theory

I'm currently taking a Discrete Math class with this textbook. I don't have any background in the subject, and my theoretical math background is limited to a Proofs course and a Non-Euclidan Geometry class. (Other than that I have the usual amount of undergraduate calculus and so on.) I think this book is fantastic. It is written in an engagingly casual style, and it uses a lot of examples and detail to work out the material. The other theoretical math texts I've used really don't do this - they expect you to treat their material more as hints to do your own work, which can be really hard for students (and is why you have a professor, after all). I can't address how well this book actually covers the various topics of discrete math, since I only know what I've learned in the course so far, but I'm very impressed with how well it spells things out. It's not exactly "light reading" (it's not Discrete Math for Dummies) but it is quite accessible.

As a teacher of discrete mathematics, I must constantly scan new books in the never-ending search for the best one with appropriate content and level. The course that I teach is required and early in the computer science major. It also provides the mathematical foundation for all of the later computer science courses. Therefore, any book that I use must demonstrate mathematical proofs, but not at too high a level. Coverage of fundamental topics such as propositional logic, sets, relations and functions; basic combinatorics and induction are a requirement. This book covers these fundamentals at exactly the level of rigor that I need. There are some proofs, but nothing that is beyond the motivated freshman/sophomore who is receiving the appropriate direction. However, I will not be adopting it because of the large amount of graph theory, which is approximately forty percent of the book. In our class we do cover some graph theory, but prefer to spend less time on it than this book would allow. Our department recently added a course in graph theory, so we only need to touch on the basics of graphs in discrete mathematics. Therefore, while the book is not suitable for my needs, it would be a perfect fit for anyone teaching discrete mathematics where there was an emphasis on graph theory. In fact, the second half of the book could serve as a starter text for our course in graph theory.

This text was designed mainly for young university students with the goal of introducing concepts such as induction to as well as, of course, some introductory descrete math and graph theory, with the former (induction, etc.) being as important as the latter. This is not a comprehensive text and was not intended to be so. It is a pleasent bridge to more mathematically correct way of thinking. Proofs are emphasized, not numerical answers (in most sections). Famous proofs are displayed and are incorperated in a non-trivial way. This book is applicable for mathematics and computer science students alike and the questions have a good spread of difficulty. I recommend this book to anyone interested in something more than high school math.