Customer Reviews

Discrete Mathematics for Computer Science (Mathematics Across the Curriculum)

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I evaluated this book for possible adoption in a course in introductory discrete mathematics. My decision was that I would not use it in the course. One primary reason is that there are no sections devoted to set theory and functions. Most of the introductory material in these areas is included in the book, but only in conjunction with other topics, such as counting, solving recurrences and computing probabilities. In my experience, students need to be exposed to the material as a point of emphasis, rather than embedded inside other topics.

The first chapter introduces the basic principles of counting, permutations, combinations, binomial coefficients and a section on equivalence relations that is considered optional. This is because it is not used again in later chapters, something I don't agree with. Chapter two deals with cryptography and number theory. While I have no objection to this material in a discrete mathematics course, I prefer that it be put off to the latter part of the course. In chapter three, the logic of propositions and predicates as well as the laws of inference are examined. I generally prefer more coverage of these areas. Chapter four is 84 pages and covers induction, recursion and recurrence relations. Taking up approximately one fourth of the book, the coverage is complete. Probability is covered in chapter 5 and graph theory in chapter 6. The coverage in both is fairly typical, so I have no positive or negative comments on either one. Relations are covered in depth in an appendix. Solutions to the odd exercises are included in an appendix.

Since I prefer to start my discrete mathematics course by covering set theory, functions and logic, I have removed this book for adoption consideration.

The writing of this book is complete garbage. Every chapter is riddled with either non-sense proofs or complete mathematical jargon. They fail to put the concepts into writing understandable to someone who isn't a mathematician. On top of that the book is very quick paced. Constantly there are several page proofs/derivations that confuse you more than help you understand the simple equation shown shortly after. The book does offer helpful "check-up" exercises at the end of each section allowing you to check if you need to make another attempt at deciphering the previous section's jibberish. All in all, if you struggle with math vocabulary I suggest to choose another book. On the contrary if you excel at math and understand math terminology with ease this book might help you quickly learn discretionary mathematics.

As an experienced teacher working on a second bachelor's in preparation for a master's, I am saddened to report this is very possibly the worst textbook I have ever seen in my entire educational life.

Two words summarize the flaws in this alleged textbook: jargon and assumptions.

Every sentence sent me to the math dictionary at least twice. I continually questioned why the writer chose not to use plain language when it was suitable, possible, and appropriate.

To make matters worse, each section begins and is riddled with exercises that assume the reader's understanding of the material. Then, the writer adds insult to injury by relying on those assumptions and referencing the opening exercises as if the exercise taught you something. Whatever happened to teach, example, and exercise? Beginning and inundating the sections with exercises that preempted the scant instruction completely convoluted the entire learning process and destroyed any sense of continuity.

In the end, to use the book I first had to try to identify what the writer was trying to teach, and that wasn't always possible. After scavenging internet math dictionaries to pin down the topic, I then had to further troll the internet to find sites that taught it in a way that would help me understand the book. Even then I had to waste obscene amounts of time sifting through exercise text to isolate the relevant instruction.

Maybe this book was written for postgraduate readers, because if you didn't know the subject matter already, you're not likely learning it from this text.

I am a professional computer scientist and, having graduated from university a considerably long time ago, I picked this book up to study the mathematics that underpins the various algorithms that we select and use. Despite such a long absence from studying mathematics, I found this book quite easy to understand and use.

The first chapter looks at counting from a practical, computing, perspective and introduces the use of sets as well as how they are applied to algorithms such as insertion sorts. The second chapter, on cryptography, can probably be omitted unless it is of specific interest. The third chapter considers logic and proofs, and is very well written. The fourth, fifth and sixth chapters deal with recursion, probability and graph theory respectively. All chapters are extremely practical as they have ample examples, using pseudo-code, that illustrate the use and analysis of various algorithms. This is done to understand the rationale, in mathematical terms, of the topic under discussion. Furthermore, every chapter ends with a set of exercises, some of which have answers or hints provided at the end of the book. All these tools give a refreshing balance between theory and practice that no other book (I have come across plenty!) on discrete mathematics comes close to in comparison. Indeed, any one chapter is worth the price of the book.

Thoroughly recommended. You will not regret buying this book as it will be a good reference even after you have studied it.