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5.0 out of 5 stars Excellent book for aspiring computer scientists
This book is an excellent introduction to math in the computer world. It is exactly what it describes itself to be and exactly what everyone told me it would be. My last math experience was in high school and so far it is proving difficult but it is fun and definitely a mind workout. I would say it might be better suited for people with a college math background but I...
Published 7 months ago by Romani Chez

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3 of 4 people found the following review helpful
3.0 out of 5 stars Only one problem with this textbook
Basically, I like this textbook. The material is interesting, the way the authors presented the material is inspiring, and they provided a lot of jokes to make even studying for exams not that boring. But there is one big problem which made me decided to rate this book only 3 stars instead of 5 stars: the authors like to use non-standard notations. For example: m\n means...
Published on April 13 2004


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3 of 4 people found the following review helpful
3.0 out of 5 stars Only one problem with this textbook, April 13 2004
By A Customer
This review is from: Concrete Mathematics: A Foundation for Computer Science (2nd Edition) (Hardcover)
Basically, I like this textbook. The material is interesting, the way the authors presented the material is inspiring, and they provided a lot of jokes to make even studying for exams not that boring. But there is one big problem which made me decided to rate this book only 3 stars instead of 5 stars: the authors like to use non-standard notations. For example: m\n means "m>0 and n=mk for some integer k". One of the worst thing in scientific world is writing things others cannot read, and the authors did this by introducing many strange notations. These things makes the good work sometimes almost unreadable. This is not computer systems in which we use "cp" for the copy command and "cd" for change directory command.
What a pity the authors did that. This textbook will be perfect without those strange notations....
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5.0 out of 5 stars Excellent book for aspiring computer scientists, Sept. 15 2013
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This review is from: Concrete Mathematics: A Foundation for Computer Science (2nd Edition) (Hardcover)
This book is an excellent introduction to math in the computer world. It is exactly what it describes itself to be and exactly what everyone told me it would be. My last math experience was in high school and so far it is proving difficult but it is fun and definitely a mind workout. I would say it might be better suited for people with a college math background but I have heard of high school students working through it. Overall an awesome book if you love to learn.
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3 of 3 people found the following review helpful
5.0 out of 5 stars Please Be Discrete, July 13 2001
By 
Mary P. Campbell "math geek" (Flushing, NY USA) - See all my reviews
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This review is from: Concrete Mathematics: A Foundation for Computer Science (2nd Edition) (Hardcover)
What is "concrete" math, as opposed to other types of math? The authors explain that the title comes from the blending of CONtinuous and disCRETE math, two branches of math that many seem to like to keep asunder, though each occurs in the foundation of the other. The topics in the book, such as sums, generating functions, and number theory, are actually standard discrete math topics; however, the treatment in this text shows the inherent continuous (read: calculus) undergirding of the topics. Without calculus, generating functions would not have come to mind and their tremendous power could not be put to use in figuring out series.
The smart-aleck marginal notes notwithstanding, this is a serious math book for those who are willing to dot every i and cross every t. Unlike most math texts (esp. graduate math texts), nothing is omitted along the way. Notation is explained (=very= important), common pitfalls are pointed out (as opposed to the usual way students come across them -- by getting back bleeding exams), and what is important and what is =not= as important are indicated.
Still, I cannot leave the marginal notes unremarked; some are serious warnings to the reader. For example, in the introduction, one note remarks "I would advise the casual student to stay away from this course." Notes that advise one to skim, and there are a few, should be taken seriously. All the marginal notes come from the TAs who had to help with the text, and thus have a more nitty-gritty understanding of the difficulties students are likely to face. Still, there are plenty of puns and bad jokes to amuse the text-reader for hours: "The empty set is pointless," "But not Imbesselian," and "John .316" made me chuckle, but you have to find them for yourself.
To someone who has been through the rigors of math grad school, this book is a delight to read; to those who have not, they must keep in mind that this is a serious text and must be prepared to do some real work. Very bright high school students have gotten through this text with little difficulty. I want to note ahead of time - some of the questions in the book are serious research topics. They don't necessarily tell you that when they give you the problem; if you've worked on the problem for a week, you should turn to the answers in the back to check that there really is a solution.
That said, I would highly recommend this book to math-lovers who want some rigorous math outside of the usual fare. The formulas in here can actually come in handy "in real life", especially if one has to use math a lot.
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2 of 2 people found the following review helpful
4.0 out of 5 stars Fear first, love later, Dec 12 2002
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This review is from: Concrete Mathematics: A Foundation for Computer Science (2nd Edition) (Hardcover)
I used this book while studying Combinatorics at the University of Warwick, a leading British institution for mathematicians. At the time, the book was a little bit overwhelming - Knuth doesn't waste any time in getting to the point of solving problems in the book. Thus, if you're the type of person who needs lots of worked examples, I would supplement this with another book, for example, Grimaldi's Discrete and Combinatorial Mathematics. But this book does belong on the bookshelf - it is a great reference, particularly because it prepares one to read The Art of Computer Programming, also by Knuth. TAOCP is the definitive series on computer science, respected by computer scientists everywhere. I guess the best way to describe Concrete Mathematics is that if you are a graduate student in CS, you should own this book. If you are a mathematically-oriented undergraduate, this book will make you really understand anything that your professors will throw at you. But, if you are not a math-lover, you will want a backup and a really nice professor :)
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1 of 1 people found the following review helpful
4.0 out of 5 stars Very hard exercises., July 29 2002
By A Customer
This review is from: Concrete Mathematics: A Foundation for Computer Science (2nd Edition) (Hardcover)
This book is great. But many excercises are too hard for non-mathematically trained reader. I can solve almost all warm-up exercises without peeking the answer. But even few warm-up excercises are virtually research one. For example, see the exercise 2.1. The answer for this exercise is that there is no agreement about this. I think it means that there is no answer for this exercise. Sometimes even understanding an answer is very hard when you read an answer because you can't solve an exercise. This book contains answers for all exercises. But this book's exercises are MUCH HARDER than many other mathematic books which contain answers for only odd number(or even number) exercises.
You need a great inductive mathematical reasoning experience to read this book. If you finish this, you can omit the first 100 pages of TAOCP vol 1.
It would be nice if there is a solution book for this hard concrete book.
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4.0 out of 5 stars So far, a good read, I can't wait to read more., May 10 2003
By 
Tim Greer "Mr. Tim" (USA) - See all my reviews
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This review is from: Concrete Mathematics: A Foundation for Computer Science (2nd Edition) (Hardcover)
And, I hope I can get the time to finish it. This is a good prelude to some of the more agressive algorithm books out there, if you take any very advanced programming courses--and gets you mroe ready for some of the Knuth books (now there's a challenge).
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4.0 out of 5 stars Enjoyable next step, Sept. 5 2001
This review is from: Concrete Mathematics: A Foundation for Computer Science (2nd Edition) (Hardcover)
I've greatly enjoyed this book. And while I haven't finished it _yet_, I can still tell you that this book is _very_ good for self study. I find myself applying what I've learned to "real" life (okay, the American Mathematics Competition -> 12). Not a bad decision if you plan to go further in math.
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5.0 out of 5 stars I keep this one always within reach, June 16 2001
By 
De Paoli Andrea (Rome Italy) - See all my reviews
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This review is from: Concrete Mathematics: A Foundation for Computer Science (2nd Edition) (Hardcover)
I found this book very stimulating, and whenever I have a chance I go back to some of the harder problems. This book should please the more mathematically oriented programmers as well as anyone with curiosity regarding numerical mathematics. The scholarship is thorough and I find particularly noteworthy the attempt to ascribe soucres correctly and I appreciated the attention to detail (even the font used).
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5.0 out of 5 stars Concrete Math--neither "abstract" nor "applied", May 15 2001
By 
M. Le Brun (Novato, CA USA) - See all my reviews
This review is from: Concrete Mathematics: A Foundation for Computer Science (2nd Edition) (Hardcover)
Lest others find this wonderful book as disappointing as the reviewer from Osan, Korea: note that "concrete" in the title is just meant in contrast to "abstract". But both concrete and abstract are adjectives intended only to describe different apporaches to *theoretical* math, as opposed to *applied* math, which addresses examples directly relevant to the real world (and thus is probably of more interest to engineers and their ilk). This *isn't* an applied math text. The difference between the concrete and abstract styles is that concrete math generally takes a "bottom up" tack, arising from specific given "concrete" entities, such as certain special functions, sums, sequences etc and tends to involve more derivation and calculation. In contrast typical abstract math is more "top down", proceeding, say, from axioms, perhaps even non-constructively, and tends to involve more reasoning and proving. If you dig the theoretical stuff, and like the concrete approach, this book is a treasure trove.
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4.0 out of 5 stars Excellent book, but lacking in some areas, Sept. 6 2000
By 
Nate (Santa Cruz, Ca USA) - See all my reviews
This review is from: Concrete Mathematics: A Foundation for Computer Science (2nd Edition) (Hardcover)
Overall this is a must-have book for anyone in CS. Besides being a great read, I've found it usefull on several occasions to solve problems and it's very likely that a CS Prof will reference this book in lecture or homework problems.
However, the books mathematical notation is sometimes unique and it is not always clear were symbols and their meanings are defined. For example, in the first chapter S_n (that's S sub n) is used in place of summation notation. Then, in the exercise solutions S_n is used again but it is expected that the reader know that this is in reference to the use of S_n in a chapter example. Because S_n is non-standard notation it would have saved me much confusion if the authors had explicitly defined S_n. This seems to happen a lot and I spent a lot of time combing through the books examples looking for definitions of symbols.
Yet, despite these problems, this book is a classic.
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