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Title: Concrete Mathematics: A Foundation for Computer Science (2nd Edition) by Ronald L. Graham, Donald E. Knuth, Oren Patashnik ISBN: 0-201-55802-5 Publisher: Addison-Wesley Pub Co Pub. Date: 28 February, 1994 Format: Hardcover Volumes: 1 List Price(USD): $57.99 |
Average Customer Rating: 4.33 (21 reviews)
Rating: 4
Summary: Excellent book, but lacking in some areas
Comment: 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.
Rating: 5
Summary: Please Be Discrete
Comment: 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.
Rating: 2
Summary: Fragmented writing style of some advanced math topics
Comment: 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.
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Title: The Art of Computer Programming, Volumes 1-3 Boxed Set by Donald E. Knuth ISBN: 0201485419 Publisher: Addison-Wesley Pub Co Pub. Date: October, 1998 List Price(USD): $149.99 |
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Title: Introduction to Algorithms, Second Edition by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein ISBN: 0262032937 Publisher: MIT Press Pub. Date: 01 September, 2001 List Price(USD): $79.95 |
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Title: Introduction to the Theory of Computation by Michael Sipser ISBN: 053494728X Publisher: Brooks Cole Pub. Date: 13 December, 1996 List Price(USD): $101.95 |
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Title: An Introduction to the Analysis of Algorithms by Robert Sedgewick, Philippe Flajolet ISBN: 020140009X Publisher: Addison-Wesley Pub Co Pub. Date: 30 November, 1995 List Price(USD): $57.99 |
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Title: The Design and Analysis of Computer Algorithms by Alfred V. Aho, John E. Hopcroft, Jeffrey D. Ullman ISBN: 0201000296 Publisher: Addison-Wesley Pub Co Pub. Date: June, 1974 List Price(USD): $54.38 |
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