Discrete Mathematics and Its Applications (7th Edition)

by Kenneth H. Rosen

Discrete Mathematics and Its Applications is intended for one or two term introductory Discrete Mathematics courses taken by students from a wide variety of majors, including Computer Science, Mathematics, and Engineering. This renowned best-selling text, which has been used at over 500 institutions around the world, gives a focused introduction to the primary themes in a Discrete Mathematics course and demonstrates the relevance and practicality of Discrete Mathematics to a wide variety of real-world applications―from Computer Science to Data Networking, to Psychology, to Chemistry, to Engineering, to Linguistics, to Biology, to Business, and many other important fields.

McGraw-Hill Education's Connect, is also available as an optional, add on item. Connect is the only integrated learning system that empowers students by continuously adapting to deliver precisely what they need, when they need it, how they need it, so that class time is more effective. Connect allows the professor to assign homework, quizzes, and tests easily and automatically grades and records the scores of the student's work. Problems are randomized to prevent sharing of answers an may also have a "multi-step solution" which helps move the students' learning along if they experience difficulty.

Genres: Mathematics, Computer Science, Textbooks, Reference, Nonfiction, Science, Programming

Paperback

First published April 1, 2000

About the author

Dr. Rosen received his B.S. in Mathematics from the University of Michigan, Ann Arbor
(1972), and his Ph.D. in Mathematics from M.LT. (1976).

Dr. Rosen has published numerous articles in professional journals in the areas of number theory and mathematical modeling. He is the author of the textbooks Elementary Number Theory and Its Applications, published by Addison-Wesley and currently in its fifth edition, and Discrete Mathematics and Its Applications

Reviews

[Erik · Rating 2 out of 5]

I'm convinced that math gurus are incapable of teaching math.

Whenever I encounter math textbooks like this one, I'm reminded of Underpants Gnomes on South Park. For the unwashed: Underpants Gnomes stole underwear from the residents of South Park hoping that they'd profit from the thefts, but although their business plan included a Phase 1 ("Steal underwear") and a Phase 3 ("Make a profit"), Phase 2—the connective tissue—was just "?".

Rosen and others like him fail to grasp how much "?" connective tissue they're leaving out when they "teach" math. He'll describe a math concept using almost-but-not-quite human language, then—oh, there's always a "then" with these books—the math gymnastics begin. Math teachers can't resist the gymnastics, can they? No, they really can't. At some point they lose their ability to see how much they assume other people know, and when that happens they cease being effective at teaching. This describes almost every math teacher I've had, and it definitely describes almost every math textbook that I've read. Rosen's book isn't the worst math textbook that I've read, but it's still pretty awful.

Seriously, corner cases and extreme mind-bending problems don't help people learn math; giving students time to grasp concepts before baffling them with bullshit does. This is why math schools like Khan Academy are amazing and college/university level math courses are not. This stuff can be taught, but not like this.

[Eli · Rating 2 out of 5]

tl;dr

If you open the book without a lot of theoretical math background, you'll have a good time with this book. It's written for computer scientists, so doesn't go heavy on the proofs and exact arguments, definitions, theorems, results, etc., but it makes itself relevant with many examples of how conepts are applied in CS.

Math people will probably be frustrated at the lack of depth, verbose yet fuzzy explanations, and redundant examples. You'll probably want something more concise.

Liked:

- (Usually) very accessible for people who aren't used to pure math (proofs, axioms, abstractness).
- Many illustrative, real-world examples
- Decent breadth of topics

Disliked:

- Skimpy proofs, interesting results are usually tucked away amongst the dozens of computational exercises. It's hard to figure out which problems are even worth doing.
- Too many examples. There are chapters where the vast majority of the text is just examples of the concept in action; in the graph theory chapter, there was a section with like 13 examples of basically the same thing.
- Shallow treatment of the math, sloppy definitions (he defines "clique" with the definition of the maximal clique), doesn't cover a lot of cool material that's appropriate to the subject.
- Slightly disorganized: the order in which graph theory concepts are described is awkward; you end up having to flip to the previous section, go through 12 examples to find a definition or theorem, and then flip back to the current page in order to remember what's going on.
- Doesn't acknowledge when facts are implicitly used despite not having been introduced yet.
- Not very good at explaining a lot of things, especially since his narration is inconsistent.

[Headsink headsink · Rating 5 out of 5]

Half a decade of my life dedicated to this.

[iris ᵕ̈ ia]

if this book, then i’m sad. converse: if i’m sad then this book. inverse: if not this book, i am not sad. contrapositive: if im not sad, then not this book. conclusion: i am sad.

[Parsa · Rating 3 out of 5]

read through most of this the past month. The book has 13 chapters and, There are better books describing each chapter(algorithms being a clear example). However, if you are short on time or money, or just want a good introduction to each topic before you explore them at full length later, this book will do. There is nothing really "bad" about this book. but at the same time, there is nothing incredible or special either. The applications, although certainty not bad, are far too simplified or short on explanations to be very useful. All in all, i think this serves its purpose as an introduction. But be prepared do dive deeper into some of these topics.

[Jake · Rating 4 out of 5]

I used this text for my discrete math course. We covered six chapters and it was quite thorough. my major complaint with it is that Rosen can be portentous sometimes with his examples. He knows he knows this subject well and he wants to impress you all the time.

I think I will keep learning from the book and I would say all in all it's a good textbook. I really want to know more about discrete probability sooner rather than later.

[Pedro Montoto · Rating 5 out of 5]

Best book on theoretic and Computer Science-applied mathematics. Period.

[Rafia]

good

[evelyn · Rating 2 out of 5]

where are the colors? where is the kindness? where is my will to keep going?
these are all questions that this textbook leaves unanswered.
for far too long i have read of the queen who never lies and three trunks labelled with different propositions, of muddy children not knowing if they are muddy, of p v q v r v s v t v w, and so on,
yet in no situation have i known what was happening.
examples take up half pages, and biographies about aristotle take up the rest. yet i cannot rest.

i need to graduate to get away from this book

[Mahmoud Ashraf · Rating 4 out of 5]

اذا كنت تبحث عن كتاب لتتعلم منه الرياضيات المتقطعه ( المنطق , طرق العد , الدوال ...) فعليك بالبحث عن كتاباً اخر غير ذلك , ولكن اذ كنت طالباً جامعياً او تريد ان تختبر نفسك وتحل المزيد من المسائل والتطبيقات فأرشح لك هذا الكتاب وبقوه يغطي الكتاب الكثير من المواضيع ويعطي امثله محلوله ثم يختبرك بمجموعه كبيره من الاسئلة بها افكار جميله .
انصح بذلك الكتاب للطلبة الجماعيين

[Oscar · Rating 4 out of 5]

The instances in which I was not very satisfied with this book have been very, very little so far. Or perhaps there was never one of them.

Quite frankly, differently from what I heard from several other reviews, I never had particular issues at either reading or following this book, except for the not uncommon overtime sometimes needed for finishing some of the exercises.

[L Mayfield · Rating 3 out of 5]

i am of the thinking that a math book must have full example for complete comprehension of it's content

[Dragify · Rating 5 out of 5]

The best textbook found for Discrete Mathematics Course and a suggested textbook for Innopolis University Students.

[Samuel Gompers · Rating 5 out of 5]

Discrete Mathematics is a field of study integral to the Computer Sciences. It lays the foundations for mathematical thinking in its coverage of proofs, it dives into relevant aspects of application ranging from recursive algorithm structure to modelling networks and efficient systems architecture for modern computing.

It was a fascinating read half of the chapters and performed many of the exercises. I found myself more confident in my reasoning skills and also a more rounded citizen of the world.

Great book!

[AH · Rating 4 out of 5]

I bought this book as a university textbook and I have to say the author has done a great job. This was by far the best book for a beginner with a basic understanding of mathematics and programming. I think however that the first chapters were wordy and a bit boring ,however since the book is trying to give an introductory account of Discrete mathematics maybe there is a need to wordy sometimes. Overall I think even beginners would really like this book and I strongly recommend this book to them.

[Joey Andres · Rating 5 out of 5]

This book should be the computer science standard for introductory to formal logic. It is easy to follow and ALOT of exercises to really create thicken those neural path in your head. Although, Calculus is not a prerequisite for this book, I still recommend having a concrete understanding of limits, differentiation, and integrals to really extract the most out of the exercises. After all, some important topics are also discussed in exercises.

[Jason · Rating 4 out of 5]

The explanations are a bit complex and convoluted, but I like the exercise provided. The student manual was very helpful. Overall, I learned more from the question/exercises than I did reading the text portions. The text was too abstract for me, though I do like the non-content aside reads (like the history aspect of things). I'm a CS major.

[Nathan]

Go to textbook for Discrete Math

[Jamie O'Neill · Rating 1 out of 5]

I'm writing a review of this textbook nearly a year after I last turned its pages upon seeing it still listed on my "currently reading" list.

And usually when I write one of these textbook reviews I come up with some one to two sentence little joke about the content that makes me smirk a little when writing these at 3 in the morning.

But no. Not this time. Why not you may ask? Because this textbook pisses me the hell off.

Now I personally had to take the class I was assigned this textbook for as a requirement for my Computer Science major. And I imagine this textbook is probably not too bad if you're a lazy-ass CS major that doesn't care about learning anything else.

Now why do I say this you may ask? Because this book SUCKS at actually teaching anything.

The author loves to do this thing where he presents information to you about a new topic or theorem or whatever and then naturally you expect that he'll then explain how or why any of the theory that he presents works or make sense right? Right? WRONG because Ken Rosen says FUCK YOU to understanding anything he's gonna write 10 pages of absolutely worthless drivel where nested somewhere in that is one sentence of actually useful information that you have to excavate from within his godawful writing. And then after that instead of writing anything actually worth reading he'll throw 5 pages of stupidly-specific examples that wouldn't be necessary IF HE'D SPEND 2 MINUTES EXPLAINING LITERALLY ANYTHING. And then when he DOES decide to actually write a paragraph explaining anything he uses the most convoluted language possible (using words he does not seem to understand the meaning of) to explain very simple ideas.

No wonder the fucker that wrote this has seemingly no presence either online or in person because if I had my name attatched to something this awful I too would completely shut myself off from society.

Now this next part may sound crazy, absolutely insane possibly, but I actually find Discrete Math to be pretty damn interesting (probably the first time this sentence has ever been written before). But as a tool for actually learning anything this book is completely worthless. I gave up about 3 chapters in when I realized my professor could explain the content better in a 15 minute lecture than 50 of Mr. Rosen's pages could.

However if you do end up owning this book worry not because it has several practical uses.

1. Doorstop - Rosen's incessant ramblings make this quite a large book, making it pretty effective at keeping a door in place.
2. Weapon - Similar to 1, the book's size makes it quite useful for self-defense purposes.
3. Fire - While I usually would not support book burning, the size of the book makes it excellent for kindling if you're ever stuck in the wilderness with your copy of Discrete Mathematics and its Applications and need to make a fire.

What really pisses me off is that this book is so bad that I just spent over half an hour thinking about my thoughts on this book and then writing this review of it. I have to wake up in a little over 5 hours and instead I'm spending time writing this review because it's just that bad.

I'm not gonna proofread this review because the author of this textbook sure as hell didn't have anyone proofread it so apologies if there are any grammatical or spelling mistakes

All of this is to say that this textbook is absolutely horrible, the author should feel eternal shame for having written it, and tomorrow I will be donating this book to my local dumpster. Good night.

[Joseph Campagna]

As a non-mathematician, I am a bit overwhelmed by the difficulty of the problem sets towards the end of each set (usually around #45-60). I have found that some of the practice problems require knowledge that is either accessed in later subchapters or requires outside help to solve.

For example, null quantification is a concept introduced WITHIN the problem set for chapter 1.4. Wouldn't it make more sense to introduce the notion of null quantification (and how to go about solving it) in the subchapter?

Regardless of my nit-picking, I plan on finishing the text as it is, from what I understand, the best introduction on the topic of discrete math for computer scientists.

[. · Rating 1 out of 5]

Review of 8th Edition:

This book, and Susanna Epp's discrete mathematics with applications, are among the worst math textbooks I have ever seen.

* Poorly written and poorly organized

* Too wordy

* Essential points are in a single sentence hidden in the middle of paragraphs of page-long examples.

* You can't find a previously read topic in too much overly wordy description. Googling is much faster.

It's ridiculous that many classes use this book. It seems a strong connection occurred between teachers and publishers.

[Tejas · Rating 3 out of 5]

Concepts are well explained for the most part but sometimes times the English seems confusing(it might be my personal experience).

When it comes to numericals that are part of examples, they are too poor. They are too straight forward and doesn't help the student to think and understand the concepts in a deeper manner.

Another annoying part is that the final answers are only provided for odd numbered exercise problems.

[Joc · Rating 1 out of 5]

This book is completely useless for learning actual mathematics. It not only fails to explain important concepts correctly, but also transmits the author's numerous fundamental misconceptions to you (if you carelessly accept them). Knuth's "Concrete Mathematics" is far better. (Also note that this book's objective is to transfer your money to the author and his publisher.)

[foktur · Rating 2 out of 5]

ayrık matematik dersi alıyorsanız ve syllabusunuzda bu kitabı gördüyseniz; çok geçmiş olsun. verilen kavramlar yüzüstü anlatılmış; sezgisellikten uzak bir şey yazıvermişler. mühendis dostlar için bir şey diyemiyorum fakat matematikçiler için ayrık matematiğe kötü bir giriş; alternatiflerine yönelmenizde fayda olacaktır diye düşünüyorum.

ps. evet, kombinatoriği beceremiyorum 😭

[Yiğit · Rating 5 out of 5]

A great book with examples from contemporary times. The build up through the book is sustained with motivational examples and relevant references. As there are examples from various disciplines of computer science, it really helps you to draw parallels. A must read on this topic.

[Sarah · Rating 4 out of 5]

This book required me to supplement with other resources, but went far deeper than any others I found. At times, the author uses the phrase, "It is easy to see how ____," which often had me yelling at the book, "No, it's not!" but ultimately, I learned a great deal from this text.

[Shahadat ক খ গ ঘ ঙ চ ছ জ ঝ ঞ, ট ঠ ড ঢ ণ ত থ দ ধ ন প ফ ব ভ ম য র ল ৰ শ,ষ স হ ড় ঢ় য় ং ঃ ঁ Hossain আঅইঈউঊঋএঐওঔ · Rating 4 out of 5]

Discrete Mathematics and its Applications is a focused introduction to the primary themes in a discrete mathematics course, as introduced through extensive applications, expansive discussion, and detailed exercise sets.

[Dayton Outar · Rating 4 out of 5]

Concepts of logic and the foundations of mathematics are communicated clearly. Excellent exercises with the solutions provided at the end of the book for each chapter. Nice book to reference every now and then when solving logic and math problems.

[Solomaya Schwab · Rating 2 out of 5]

For the average student, this will do (it is especially well-suited for self-study). However, one thing that must be noted is the author's tendency to ramble. If you're looking for a concise reference book, this is not the one.

[Joseph D'Aquisto · Rating 4 out of 5]

Not My Best Subject But..
Math is not my skillset, but I used this textbook for Discrete Math I at College of Charleston back in the early 2000's. I did pass the course. While I did not understand every concept, the book was adequate enough for the course.