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Concrete Mathematics: A Foundation for Computer Science (2nd Edition)
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Author: Ronald L. Graham, Donald E. Knuth, Oren Patashnik
List Price: $59.99
Our Price: Click to see the latest and low price
ISBN: 0201558025
Publisher: Addison-Wesley Pub Co (28 February, 1994)
Edition: Hardcover
Sales Rank: 6,792
Average Customer Rating: 4.33 out of 5
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Customer ReviewsRating: 2 out of 5
Fragmented writing style of some advanced math topics
This statement from a previous review:
"Very bright high school students have gotten through this text with little difficulty"
I dare you to present Hypergeometric functions in front of a highschool student... Most graduate students would be challenged with that!This text is neither beautiful or elegant, and the little cutesy notes in the margins are distracting and childish.
(they are more memorable than the actual text) Once the simplistic Towers of Hanoi and Josephus problem are presented, the authors totally ignore any problem solving and just blast into pure mathematical manipulations that are uninitiated. Why bother with a trivial example at first, and no examples for the remaining most difficult concepts? Throughout the text are statements like "Some sequences of numbers arise so often that we give them special names"
Oh really? Where and why do they occur?
What about the sequences that do not occur frequently? The authors see no need to explain this. (Knuth: check out my expensive 3 book series, and dig for a few months) And statements in the middle of chapters like: "We now come to the most important idea in the whole book: generating functions."
Oh really? Why are they so important? (this is never explained) If so, why doesn't it have its own chapter, instead of being buried in a chapter on binomial coefficients without a lead-up? Find a closed form for:
f[n] = f[n-f[n-1]] + f[n-f[n-2]]; where f[n] = n/2
(You could memorize and learn all the math in this book, and it would never help to solve this. It handily skirts the tough fundamental questions about math.) I've never read a more fragmented presentation than this book, for important concepts. You get the distinct impression of little kids "tee hee, look at the cool manipulations I can do, and you cant...see how smart I am??"....Knuth is laughing all the way to the bank.
Rating: 4 out of 5
So far, a good read, I can't wait to read more.
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).
Rating: 4 out of 5
Fear first, love later
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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