Discrete Mathematics and its Applications

True to the Fourth Edition, the text-specific web site supplements the subject matter in meaningful ways, offering additional material for students and instructors. Discrete math is an active subject with new discoveries made every year. The continual growth and updates to the web site reflect the active nature of the topics being discussed.

The book is appropriate for a one- or two-term introductory discrete mathematics course to be taken by students in a wide variety of majors, including computer science, mathematics, and engineering. College Algebra is the only explicit prerequisite.

I found that this guide was a must have companion to "Discrete Math and Its Applications." It has the worked out solutions to many of the exercises in the text, which is very helpful. All-in-all, a definite must-have suppliment to the text.


The best book in the field   April 19, 1999
15 out of 17 found this review helpful

I have used all four editions of Rosen's book with much success with mathematics and computer science students in discrete mathematics courses for over ten years. Discrete mathematics should not be approached as a cookbook subject, and Rosen does not take a cookbook approach to the material in his book. Students are not spoonfed; they need to work carefully through the text. Rosen is very successful in helping students learn to think mathematically. Students who are serious about their study of discrete mathematics and computing will profit greatly from working through many of the more than 650 well-chosen examples and applications, ranging from easy to difficult. The new fourth edition has added many new applications, including system specifications, Web searching, and the reve's puzzle. The exercises (over 3000) are unequaled in any other discrete mathematics textbook --- they range from elementary and routine to very challenging. Answers to odd-numbered problems are in the back of the book. The new accompanying Web site includes over 250 additional exercises with answers; its many features are certainly worth exploring. A very student-friendly Student Solutions Guide provides detailed solutions to the odd-numbered exercises with much additional information on the material and how to approach it. Especially noteworthy is a companion paperback, "Applications of Discrete Mathematics" (McGraw-Hill, 1991) edited by J. Michaels and K. Rosen, consisting of 24 chapters, each devoted to an interesting application of discrete mathematics and well-suited to either classroom coverage or individual reading; some examples are bin packing, coding theory, Catalan numbers, legislative apportionment, network survivability, graph multicoloring.


The right mix of theory and applications.   March 3, 2005
Charles Ashbacher (Marion, Iowa United States(cashbacher@yahoo.com))
10 out of 12 found this review helpful

Textbooks for discrete mathematics define a broad spectrum in terms of the level of difficulty. At the lower end, there are the books that present the theorems, but rarely if ever include a proof. Then, armed with the theorem, it goes on to apply the theorem to solve the appropriate problems. At the higher end, there are the books that follow the theorem-proof design, with a smaller number of applications. This one is at the higher end; there are very few theorems that are not proven.
Following the trend in computer science, the breadth of coverage in discrete mathematics has also increased over the years. This is reflected in the size of the book, the text section, without appendices, solutions and index is almost eight hundred pages. The coverage is complete, and it starts exactly where it should, with logic, basic set theory and functions. After that, there is a chapter on algorithms and matrices, one on proof strategies with induction and recursion, three chapters covering counting principles and discrete probability, and ending with chapters on relations, graphs, trees, Boolean algebra and modeling computation.
The explanations are sound, although the mathematical depth is a bit on the high end, which no doubt explains some of the very negative reviews. There are many exercises at the end of the sections and solutions to the odds are included in an appendix. In my opinion, this is an absolute necessity, I will not even consider a book that doesn't include the solutions to many of the problems. At the end of each chapter there is a set of supplementary exercises, a list of projects to be solved by writing a computer program and a list of suggested writing projects.
What I liked most about the book has nothing to do with the discrete mathematics. The author included a large number of brief biographical sketches of mathematicians. When I was looking the book over for the first time, I paged through the book reading every one the biographical shorts. Nevertheless, this is one of the better books in the field of discrete mathematics, with large amounts of time spent on both the theory and applications, it has just the right mix to satisfy both tastes.



The "Violin" Book of Discrete Mathematics   August 6, 2002
Todd Ebert (Long Beach California)
21 out of 29 found this review helpful

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.


The best math text I've ever used!   February 18, 1999
2 out of 2 found this review helpful

I'm taking a course in discrete math at Monmouth University. I was really worried about the course, but this textbook helps make discrete interesting and understandable. The author motivates the subject with so many relevant applications that he's made me understand why the subject is important for computer science. The biographies are great too. I've also checked out the Web site and it's awesome. When I've had trouble with exercises, I've found the Student Solutions Guide to be really, really helpful. This is just about the only math textbook that I ever could read and understand.