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Rating: 
Summary: No logic, few proofs makes it inappropriate as a textbook
Review: If you are looking for a book for a course in discrete mathematics where the emphasis is on graph theory, then this book will probably satisfy your needs. However, for any other type of course, it will most certainly prove to be inadequate. Nearly half the book is devoted to graph theory, and while many theorems are listed, very few are proven. The working computer scientist may find that acceptable, but most mathematicians will find it inadequate. Logic and the basics of proof are relegated to an appendix.
The first chapter covers some combinatorics and the basics of algorithmic analysis, which is meant to be a primer. However, it requires the use of set terminology, set notation and basic counting techniques. Since set theory is covered in chapter 2 and counting techniques in chapter 7, I consider the order to be inappropriate. Recurrence relations, circuits and finite state machines are also covered in other chapters.
There are a large number of exercises and the solutions to the odd numbered ones are included. Sets of problems to be solved by programming a computer are given at the end of each chapter, some of which are easy, but many of which are hard. Only students who have had a programming course could be expected to be able to do any of them without significant help.
This is a book that does not satisfy my requirements for a discrete mathematics textbook. I consider logic to be a critical topic that must be covered, so I will not consider using any book where predicate and propositional logic are not covered in depth. While I do not expect my students to construct rigorous proofs, I do expect them to be able to construct simple proofs and follow some of the relevant more complicated ones.
Rating: 
Summary: Good except for its coverage of mathematical induction
Review: The discrete math course at our university is a sort of "rite of passage" for math majors- it introduces students to the idea of proofs, as well as basic set and graph theory and combinatorics. It is an introduction to the abstract aspect of mathematics. This book serves this purpose well, with a number of examples and drawings to illustrate concepts. However, this book explained induction in a manner that confused me. Also, our department wasn't too fond of this book- they switched to another after one semester. Still, I don't think it's too bad- unless the current book that the department uses is that much better.
Rating: 
Summary: Inadequate for a textbook
Review: While this book by Dossey may serve as a self-teaching book for surveying topics in discrete mathematics, it is not thorough enough even for an introductory course, thus inadequate for a textbook. FYI, I am currently taking a discrete mathematics course using a popular textbook "Discrete mathematics and its applications" by Rosen.The most basic foundation of discrete mathematics is logic and proof. This part is found in the very first chapter of Rosen book. On the contrary, Dossey book covers that part in the appendix! While one may read the appendix first, doing so is still not helpful because all the proof in this book are not based on the arguments in the appendix. Also, the appendix does not cover quantifier at all. As a result, one cannot build a concrete foundation, and without it, your understanding of discrete mathematics will not go far. I do not like all aspects of Rosen book (there are some issues, as can be seen from its review), nor I like books with high level of mathematical sophistication, but I am glad that my instructor did not choose this Dossey book as a textbook. Also, its price is too high for its relatively slim volume.
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