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 | | Discrete and Combinatorial Mathematics: An Applied Introduction (4th Edition) by Ralph P. Grimaldi ISBN-10: 9780201199123 ISBN-10: 0-201-19912-2 ISBN-13: 9780201199123 ISBN-13: 978-0-201-19912-3 Hardcover 1998-10 Addison Wesley Publishing Company Find Lowest Price |
Reviews | ||
Do not buy this book. This book is very poorly written and lacks any kind of order in which to study the chapters. The explanations of theorums and formulas are just not enough. Another thing that I do not like about this is that the section problems want you to work out precise mathematical concepts that were not explained in the relevant section, thus making you have to re-read the section several times over, and even then it is still not enough. I have completed Calculus II and that textbook was nowhere near as difficult to understand than this one. If you want to get a general idea of what Discret Mathematics is or want to do self study, then get this book. But in my opinion, avoid this book at all cost. Pun intended. | ||
More rigorous and lengthy than other discrete texts, too much for my purposes I will once again be teaching discrete mathematics this summer, so I am searching through the mathematical publishing pathways looking for a suitable textbook. Therefore, that is the context within which I examined this book. It certainly is the largest discrete book that I have encountered; including the appendices and problem solutions, there are over one thousand pages. Grimaldi has tried to include every topic that falls under the discrete mathematics tent. Therefore, this is a book that could be used for a two semester sequence in discrete mathematics. When examining discrete books for possible adoption I start with the simple premise that logic, set theory and functions and relations must be covered very early. In my ideal world, they are the first three chapters. Set theory and relations are so fundamental a part of other areas that I am surprised when authors don't cover them first. The first chapter in this book covers basic counting principles. While this doesn't break too much from my ideal sequence, I see no overpowering reason why fundamental counting should be before set theory. Given that the rules of counting for sums and products can easily be related to sets, there is a strong justification for putting set theory first. The coverage is split into four parts, the first of which consists of the seven chapters: *) Fundamental principles of counting *) Fundamentals of logic *) Set theory *) Properties of integers: mathematical induction *) Relations and functions *) Languages: finite state machines *) Relations: second time around In my opinion, the order of the topics should be: *) Fundamentals of logic *) Set theory *) Relations and functions *) Relations: second time around *) Fundamental principles of counting *) The principle of inclusion and exclusion (currently chapter 8) *) Properties of integers: mathematical induction *) Generating functions (currently chapter 9) *) Recurrence relations (currently chapter 10) *) Languages: finite state machines The current chapters 8 through 10 make up part two of the book. Part three is graph theory and applications and part four is modern applied algebra. I have no issues with the order here. The chapter headings for the fourth part are: *) Rings and modular arithmetic *) Boolean algebra and switching functions *) Groups, coding theory and Polya's method of enumeration *) Finite fields and combinatorial design With this part being nearly two hundred pages in length, the coverage is extensive. Grimaldi takes a more rigorous approach than many other authors of discrete texts, while I did not examine every single theorem, I did look at a lot of them and all were accompanied by a proof. The exposition is clear, there are many worked examples, a large number of exercises and solutions to the odd-numbered exercises are included. A summary and historical review of the topic follows each section. If we offered a two course sequence in discrete mathematics, then I would consider adopting this book. Such a situation would allow me to present the material at a higher level of rigor, where this book excels. However, with a one semester course designed to teach computer science majors the mathematical fundamentals they need, this book is both too long and too deep. | ||
ideal for self study Excellent book, carefully chosen examples, ideal for self study. I like it very much. My advice is not to skip any section or solved examples or you might be lost. | ||
Maybe it's just me I find this book lacks explanation at many points, to where I couldn't understand thw way the author presented a problem, a subject, etc... I almost feel like the target audience is to other college professors, and not students of the subject. I also don't like that a lot of the harder problems at the end of the sections are even numbered, so that you don't have a way to see how they are worked. I don't really feel the book warrants just one star, but since most people in my class don't care much for the book, I am confused to all of the great reviews on this web site and felt I needed to show the contrast that my class experienced with it. I think the book requires a good instructor to help you get through it, in contrast to the comments to others who have said it's good for a self learner. I am also enrolled in Calculus 2 and Linear Algebra, and the books I am using for those courses are FAR superior to this one. and I have missed a few class sessions in those two courses and am still running a high B and a mid A in those courses. I wouldn't dream of missing a class in the Discrete Math class because I feel too dependant on the instructor's explanations. | ||
great book on discrete math This is an excellent book for self study. However, there are parts in this book that must be rearranged or deleted. For example, I think Catalan numbers should be deleted. This might be useful for the matrix chaining problem, but that's in the realms of algorithm design (specifically in dynamic programming). Also, I do not understand why Grimaldi sandwiched in a chapter on Finite State Machines between two chapters on Functions and Relations. Maybe he should make a section on languages for FSMs, but I recommend Sipser's Introduction to the Theory of Computation if you want to learn about FSMs. | ||