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Concrete Mathematics: A Foundation for Computer Science
 
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Concrete Mathematics: A Foundation for Computer Science (Hardcover)

by Ronald L. Graham (Author), Donald E. Knuth (Author), Oren Patashnik (Author)
4.2 out of 5 stars  See all reviews (21 customer reviews)
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Product Description

This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories.Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include: *Sums *Recurrences *Integer functions *Elementary number theory *Binomial coefficients *Generating functions *Discrete probability *Asymptotic methods This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them. 0201558025B04062001


Ingram

This book, updated and improved, introduces the mathematics that support advanced computer programming and the analysis of algorithms. The book's primary aim is to provide a solid and relevant base of mathematical skills. It is an indispensable text and reference for computer scientists and serious programmers in virtually every discipline.

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Customer Reviews

21 Reviews
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Average Customer Review
4.2 out of 5 stars (21 customer reviews)
 
 
 
 
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3 of 3 people found the following review helpful:
5.0 out of 5 stars Please Be Discrete, Jul 13 2001
By Mary P. Campbell "math geek" (Flushing, NY USA) - See all my reviews
(REAL NAME)   
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
By William Stevenson (State College, PA) - See all my reviews
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., Jul 29 2002
By A Customer
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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Most recent customer reviews

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... Read more
Published on April 13 2004

2.0 out of 5 stars 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... Read more
Published on Sep 22 2003 by torontobikerboy

4.0 out of 5 stars 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... Read more
Published on May 10 2003 by Tim Greer

4.0 out of 5 stars Enjoyable next step
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. Read more
Published on Sep 6 2001 by a butt

5.0 out of 5 stars I keep this one always within reach
I found this book very stimulating, and whenever I have a chance I go back to some of the harder problems. Read more
Published on Jun 16 2001 by De Paoli Andrea

5.0 out of 5 stars Concrete Math--neither "abstract" nor "applied"
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... Read more
Published on May 15 2001 by M. Le Brun

4.0 out of 5 stars Excellent book, but lacking in some areas
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... Read more
Published on Sep 6 2000 by Nate

5.0 out of 5 stars Excellent, but not worth that much.
This is indeed an excellent book and if you lived in Bangkok, you could buy this very same book for about twelve dollars. I just did so today.
Published on Aug 9 2000 by Andrew Criswell

4.0 out of 5 stars Bad fonts
I can't find another book that covers similiar material at this depth. A great book possibly a future classic but unfortunately the font ("Euler" font which was created... Read more
Published on Mar 31 2000 by esseyo

5.0 out of 5 stars Useful and well-written
This is one of those books you keep forever, purely for its utility: it's packed with formulas, techniques, examples. Read more
Published on Jan 30 2000 by Naomi Novik

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