- Hardcover: 896 pages
- Publisher: Pearson; 4 edition (19 Nov 1998)
- Language English
- ISBN-10: 0201199122
- ISBN-13: 978-0201199123
- Product Dimensions: 24.3 x 19.9 x 4.2 cm
- Average Customer Review: 3.0 out of 5 stars See all reviews (1 customer review)
- Amazon Bestsellers Rank: 2,137,886 in Books (See Top 100 in Books)
- See Complete Table of Contents
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Product Description
This fourth edition continues to improve on the features that have made it the market leader. The text offers a flexible organization, enabling instructors to adapt the book to their particular courses: discrete mathematics, graph theory, modern algebra, and/or combinatorics. More elementary problems were added, creating a greater variety of level in problem sets, which allows students to perfect skills as they practice. This new edition continues to feature numerous computer science applications-making this the ideal text for preparing students for advanced study.
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Customer Reviews
Most Helpful Customer Reviews
3 of 5 people found the following review helpful
Format:Hardcover
This is an average book. I am currently in the third year of an engineering mathematics course. This was not the recomended text. But that text was terrible in comparision to this which is also not a great book. The explanations could be clearer, and better laid out. But this book is useful as a reference, when really really confused. In my opinion more examples would be usefull as this text has few.
Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com:
36 reviews
15 of 16 people found the following review helpful
A math book that's actually understandable
24 April 2000
Format:Hardcover
Finally! A math book which is acutally well written, has enough examples to illustrate key concepts, and has enough problems to keep the math student busy. Discrete mathematics is a fairly involved subject and books on the topic range from relatively basic to extremely difficult treatises which only a PhD or a math professor could understand. Discrete and Combinatorial Mathematics : An Applied Introduction by Ralph Grimaldi is a book which will appeal to both sides of the spectrum. The book is written so that most undergraduate students will have little difficulty understanding, but graduate students will also find it indispensable as a reference. The illustrated examples are actually relevant to the homework problems, which is often missing in mathematical texts. Finally, the book does not try to overwhelm the reader with lofty proofs or stilted language. Each chapter builds on the previous subjects learned. That's all I can ask for in a math text. I like the coverage of combinatorics in the first chapter, which does a better job than many probability textbooks. And be sure to understand Euclid's theroem and the examples given in the book. Quite a few high-tech companies will ask you about the problem Grimaldi gives as an example of Euclid's theorem in their job interviews.
10 of 10 people found the following review helpful
More rigorous and lengthy than other discrete texts, too much for my purposes
16 Jan 2007
Format:Hardcover
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.
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.
12 of 13 people found the following review helpful
ideal for self study
25 Jan 2006
Format:Hardcover
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.
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