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Rating: 
Summary: Instructive, informative and a wealth of information
Review: First some background: I'm not a math major or someone with a lot of experience in math. I can't speak about the usefulness or benefit of this book as an introduction to more advanced dicrete math topics because I've never studied anything more advanced. What I can tell you is that I used this book a couple of years ago when I returned to school after 20 years to finish my Bachelor's degree. I found the book useful and quite adequate to learn the basics of the subject, and this book was one of the reasons Discrete became my favorite math class. There is a ton of material packed in between the covers -- mathematics history, biographical sketches, spartan but helpful illustrations, web links, additional book and periodical resources -- everything you need to get through the course and more. Be warned though -- the first two or three chapters are kind of dry and difficult. Rosen explains things, but he doesn't spoon feed you. There's quite a bit of vocabulary and new ideas to digest; mathematical induction is just plain hard to understand in the beginning and it takes quite a while (and a lot of practice) to learn to construct well-formed proofs. Do yourself a favor and spend the extra money on the solution manual. What you don't understand just by reading the text is usually, though not always, made much clearer by working through the problems while reviewing the answers with the solution process laid out for you. WORK A LOT OF PROBLEMS. You will never really understand the concepts or retain the information without spending hours wrestling with this stuff. This isn't Art Appreciation 101 or Intro to Government. You're not going to grasp everything just by attending class and (maybe) reading the book. You've got to do some real analytical processing and wear out some erasers. You can fake your way through some classes, but this isn't one of them. Once you get through the first three chapters, the rest of the book goes much more smoothly. Maybe you're acclimated to the subject by this time and it just comes to you easier. If you're like me, you should really begin enjoying things at this time and seeing how this can actually be useful in terms of understanding computation and computer science. You also begin to appreciate the organizational and teaching style of the book. It progresses at a good pace, but provides enough intoductory information and exercises to keep you from feeling like a complete idiot once you reach the more advanced sections in the chapter. Sure, there are some rough spots and a few sections that you just have to re-read several times. This IS a math text -- you can't expect it to be a page-turner like a good novel. For those reviewers who think this book is too theoretical or too terse or just a pile of proofs thrown on top of each other, they need to open some of the other higher level math books out there. This book may not be perfect, but it was pure joy compared to my nightmare experience with numerical analysis (Numerical Analysis and Methods by Epperson). As for the cost, the book is way over-priced, but then what text book isn't? It just comes with the territory.
Rating: 
Summary: Well I liked It
Review: I like the layout, I like the explanations, I like the coverage. It's my favorite textbook. But the material isn't easy, and I think this will always mean Discrete Math textbooks get low reviews.
Rating:
Summary: The "Violin" Book of Discrete Mathematics
Review: This book easily ranks as my favorite lower-division math/computer science textbook. Aside from its omission of elementary coding theory, this book contains just about every important discrete mathematical topic (logic, sets, functions, algorithms, complexity, combinatorics, relations, graphs, Boolean algebra, formal language theory) that a beginning student should be introduced to. Plenty of examples in each section that reflect the end-of-section exercises. Very well organized in that key definitions, rules, and theorems are boxed and well highlighted.
Concepts are well explained and reinforced with numerous examples.
And most importantly, plenty of engaging problems that range from trivial to quite challenging. Applications to areas such as computer science are in abundance. But most enjoyable for me are the numerous biographical sketches of important discrete mathematicians. All around an excellent text, and one I had been searching for since my days as a freshman in college when I had wondered when, as a math major, I would ever get to the fun stuff: logic, graphs, codes, etc.. Little did I know that I would have to wait 17 years as a professor at the same college to finally get to it.
Rating:
Summary: Excellent Discrete Math book
Review: This is a very good book on Discrete Math. I have looked at several books and the only other book that comes close to quality is "Discrete Mathematics" by Hein.
To get the most out of this book it is recommended to get the solutions manual. Also the book's website has several useful worked out examples and links. Discrete Math is what computer science is all about and if you don't like Discrete Math then you should stay away from CS.
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