Discrete Mathematics with Applications

I have read "Discrete Mathematics" by Epp, Rosen and Ross which are the three most common discrete math texts that I encounter at university. Of these three, I would rate Epp's book as my favorite because it has the clearest explanations and is so easy to read that you can't help but feel like you understand all of the content completely. The only failing that Epp's book might have is that it is not as thorough in its coverage of the material as some of the more technical books. I would say that it covers about 90% of the material and leaves out some of the more obscure topics. Rosen's book would be the most thorough, covering every topic in meticulous detail and offering a jumping point for other texts in cryptography and number theory. Although this book is more complete than Epp's, it is also less readable and requires more effort to get through. Ideally you would use Epp's book to learn the material and then go to Rosen's book for a technical reference. For those of you who are considering Ross's book, I have one thing to say and that is don't. Although I have read this book and done a lot of the problems in the first 3/4 of the text, this book is neither clear in its explanations like Epp nor is it as complete as Rosen's book. If you are assigned this book for a course, my suggestion would be to buy Epp's book and photocopy the Ross homework problems from a friend's textbook. Take the advice of someone who has read all three books. If you have to buy just one, then get the Epp book. It is better to understand 90% of the material completely rather than 100% of the material partially.

I used an earlier edition of this textbook in a discrete mathematics class that was required for those of us with a non-CS background enrolled in a MSCS program at Virginia Tech, and I found this to be an excellent and complete book on the subject. If you find yourself enrolled in a class using this book, you can be sure of two things - your instructor knows how to select good textbooks and also it won't matter if your instructor is a good teacher since this book does all of the work for him/her. If you are enrolled in a class on discrete math and this textbook is not assigned, might I suggest you get a used copy of the previous edition. It is just as good as this current edition and used copies can easily be found dirt cheap. If you buy a copy of a previous edition the topics you'd be missing that are new to this edition would be expected value, conditional probability, Bayes' theorem, modular arithmetic, Fermat's little theorem and the Chinese remainder theorem, and RSA cryptography. The author has included illuminating examples of all concepts throughout the textbook, defined all terms, and makes sure that each new concept introduced builds on previously explained material. Subjects covered include the logic of computation, including the predicate logic that is necessary for fully understanding artificial intelligence, methods of proof including the method of induction and also the terminology of sequences, number theory and combinatorics, O-notation and the calculation of the efficiency of algorithms, graph theory and discrete structures, and an introduction to concepts from the theory of computation. There are many exercises included, with the solutions to selected exercises in the back of the book. This book only assumes mathematical maturity at the level of precalculus, excluding trigonometry. I highly recommend this text especially to students who are transitioning to computer science from some other discipline and need a firm foundation in the basics of that field. You'll find it useful as a foundational text for studying artificial intelligence, the theory of algorithms, mathematical models of computation, and the theory of computation. Another useful book on this subject is the "Schaum's Outline of Discrete Mathematics". The table of contents are as follows: 1. The Logic of Compound Statements 2. The Logic of Quantified Statements 3. Elementary Number Theory and Methods of Proof 4. Sequences and Mathematical Induction 5. Set Theory 6. Counting 7. Functions 8. Recursion 9. O-Notation and the Efficiency of Algorithms 10. Relations 11. Graphs and Trees 12. Finite State Automata and Applications

This book is well written, it contains good examples, and excellent exposition. This was my introduction to mathematical proofs, and after studying it well, I was able to approach more advanced courses, such as advanced calculus and modern algebra with a clear view of how to approach problems where a mathematical proof is needed. I highly recommend this book to undergraduate math majors.

This was the required textbook for my 100-level CIS discrete mathematics course, and was simply the best math text I've ever been forced to read. The examples were, at times, even more clear than my professor's explanations, and made the painful prospect of learning math much more palatable.The examples and explanations are clear, unburdened, and progresses nicely in difficulty levels. The lone drawback is that we routinely discovered blatantly incorrect answers in the professor's solutions-book while going over problems in class. A minor stain upon this most impressive (and almost enjoyable)work.

This is a neat, complete text. The author is especially sensitive to the needs of the beginner in discrete maths who needs to get used to abstract concepts. This transition is handled very well. There is enough explanation to make you understand what is going on behind the mathematical symbols and at the same time it is not wordy. Despite this simplicity in the teaching approach, the author is able to take the reader from the elementary to quite advanced levels in each topic. There are interesting applications to the field of computer science and programming.The exercises are designed to test your understanding and a few challenge problems are thrown in. This type of accessible difficulty in the problems builds your confidence. The solutions are quite elaborate and therefore make the book more useful.On the whole a good, self contained book written such that you will understand each page and concept if you have a reasonable attention span. The author has made it as easy as possible for you.Please note I have reviewed the first edition of this book as I found this edition rather expensive.