This is by far my favorite math book. I was introduced to it in a Putnam preparation course and didn't buy it at first (seemed too over the top). I found it in the library and used the school's book for some assignments. After a few nights studying out of the book I went off and bought it for myself, (half price, what a steal!) Granted, the book isn't for everyone, but if you even a glint of interest in discrete mathematics, you should definitely pick this book up.<br><br>I have not yet worked by way through the whole book (I've only solidly covered a sixth of it, but I've referenced about three quarters of it over the course of owning it). Here's what I like the most about the book:<br><br>- Good density / readability trade-off. Some math books are dense to the point that each page should take you an hour or more to fully understand. This isn't THAT bad, but it is definitely denser than your first year calculus texts. If you're used to breezing through a chapter that covers 2-6 concepts followed by some practice problems, you're going to have to get used to slowing down and doing some serious re-reading. I would estimate that getting a good grasp of each chapter takes about 20 to 60 hours of work, depending on how strong you are with the material. This includes time for solving the problems at the end of the chapter. This may sound like a lot, but trust me when I say you will know all the tricks of the trade when you're finished.<br><br>- Intuitive approach. I find many texts will spend a lot of time walking through the material in a very linear fashion. In the sense that the organization of the material makes sense once you've absorbed it, but seems random and un-ordered as you learn it. This book is ordered very intuitively the first time you read it, in the sense that the ideas seem to flow where your mind does when you first pick up the material (does this make sense?) Most chapters open with a (refreshingly tough) problem and you are walked through the solution as you learn the techniques you need to solve it. You'll pick up some very powerful problem solving techniques as you read this book.<br><br>- Good depth. Instead of telling you how to manipulate certain classes of sums, the authors go deep into the powers at work behind the problems, as well as "tricks of the trade". Some of the sum manipulations I've learned in this book I have yet to see elsewhere, and they're very handy! For example, a type of "discrete calculus" is defined, which will let you find the closed form for the sum of integers (1 through n) to the power of k with remarkable ease (it uses stirling numbers, I'm sure you can find it on the net.)<br><br>What I don't like about it:<br>- Doesn't take a very deep plunge into number theory. Covers the basics very well, but wont get you into RSA.<br>- Does not blend in continuous mathematics as well as I'd hoped.<br><br>In short, this book covers basic topics in discrete math very well. After reading this book you will be extremely comfortable manipulating sums, discrete probabilities, and number theory. It also gives you a surprisingly in-depth look at discrete math you don't often encounter in your undergraduate courses, including:<br>- Floor / ceiling functions and manipulating them.<br>- Binomial coefficients (n choose k).<br>- Generating functions.<br>- Special numbers (stirling, fibonacci, harmonic, etc.)<br>- O-notation (this is where the computer science finally kicks in).<br><br>Do read this book if you are:<br>- A math undergraduate.<br>- Someone who enjoyed math but lost touch with it long ago.<br>- Someone raised on continuous mathematics (calculus, high school math, analysis) looking to diversify their thinking.<br>- Into prime numbers, fibonacci numbers, or curious mathematical patterns.<br><br>Don't bother with this book if you are:<br>- Dumb.<br>- A math genius.<br>- A computer whiz but don't enjoy math (despite the "foundation for computer science" line, this is purely a math book).<br>- An engineering student who only cares about the answer, not the process (see the one star guy).<br>- Note: This book doesn't use the lemma - proof - example format you may be used to. You've been warned.<br><br>This book is extremely well written, and I guarantee that if you're in the "read this book if" list you will find this book impossible to get rid of, it will haunt your bookshelf for life.<br><br>Also, concerning the title. There seems to be some confusion as to why it is called "Concrete Mathematics" (see one star guy). It isn't called that because it presents, everyday, formula-solution math. The reason it's called "Concrete Mathematics" (and I quote from the preface) is because "It is a blend of CONtinuous and disCRETE mathematics." That's by far the silliest book-title formula I've ever encountered, but to each their own I guess.<br><br>And finally, I didn't see a table of contents on the order page, so I will summarize the table of contents here, in order the topics are presented:<br>- Recurrence<br>- Sums<br>- Integer Functions (floor, ceiling, modulo)<br>- Number Theory<br>- Binomial Coefficients (n choose k)<br>- Special Numbers (Stirling, Eularian, Bernoulli, Fibonacci, and others)<br>- Generating Functions<br>- Discrete Probability<br>- Asymptotics (O notation)<br><br>There's just under 500 pages of good stuff before you hit the answer to exercises. Oh yeah, there's also no flimsy "answer to odd number exercises" back page. Each problem is solved ENTIRELY, some solutions take over a page. If that's not the best way to learn, I don't know what is. Enjoy.