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Summary: Web site for all Knuth's books (incl errata etc..)
Review: is: http://www-cs-staff.Stanford.EDU/~knuth
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Summary: Concrete Math--neither "abstract" nor "applied"
Review: 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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Summary: amazing book, each time you open it you find something new
Review: most interesting book , I liked the part
about integer functions & number theory very much.
I hope that the part on integer functions will be expanded in future editions..
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Summary: Excellent book, but lacking in some areas
Review: 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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Summary: An Incredible Book
Review: This book is a gem. It provides a further level of understanding not necessarily accessible to those taught the topics of the book in a standard format. For example, one can learn techniques such as induction and perform them a formal near mechanical fashion WITHOUT understanding the WHY of the behavior of relationships being proven. This book gives you that further level of WHY.
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Summary: Very good but w/o sufficient detail in one area
Review: This book is an excellent introduction to the mathematics of algorithms, and besides featuring an engaging, chatty style, is for the most part accessible to people who do not have a tremendous amount of mathematical preparation. Some calculus is helpful, but the authors develop most of their proofs from first principles, so if you took "Calculus for Liberal Arts Majors" while in college you should still be able to learn a great deal from this book if you are interested. The only problem is that in discussing the "Repertoire Method" of solving recurrences, they never really give a top-down presentation, and we're expected to figure it out by an example. This is unfortunate because later parts of the book build on this. ANYONE OUT THERE WHO'S SEEN THIS AND IS WILLING & ABLE TO HELP PLEASE CONTACT ME. However, all exercises are solved, most in reasonable detail, which makes the book particularly useful for those who for professional or other reasons develop an interest in mathematics later in life.
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Summary: Very hard exercises.
Review: 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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Summary: Excellent, but not worth that much.
Review: 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.
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Summary: The title of this book is greatly misleading.
Review: This is not a book on CONCRETE mathematics. If it were a book on concrete mathematics, then the authors would show how the techniques described in the book arise from having to solve real-world, CONCRETE problems that arise in science or engineering. I did not find a single example of a real-world problem in the entire book. As an engineer I have zero interest in solving abstract mathematical problems such as the Tower of Hanoi problem. Show me instead a real-world problem which I can use the recurrance relation technique to solve and I will be happy to learn the technique. If a student wants to make use of this book, he or she has two choices: A) learn the techniques in the book and take it on faith that they will someday prove useful (a great approach for those who are strong believers in the spiritual world, but perhaps not very suitable for the average engineer interested in solving real-world problems) B) Research every technique described in the book to find examples how it is used to solve real-world problems (an approach that will be extremely time consuming) I don't think the average engineer, scientist, or programmer will find either of those approaches very palatable. Human beings learn best from specific to general: if you want to teach me a mathematical technique first show me how I can use it to solve a specific problem, then second show me how I can generalize that technique to solving other problems. The problem chosen should not be expressed in purely mathematical terms, but rather should be an example taken from chemistry, or physics, or computer programming, or biology, or some similar problem domain, and it should be possible to relate the results achieved with the technique back to that domain (both as an aid to understanding and to allow a check on the results). Mathematics, after all, is a tool we use to explain and describe the world we live in, and hence should be explained in terms of that world. If this approach is followed when teaching a mathematical technique, then students will learn faster, have a more thorough understanding of the technique, will be better able to remember it, and will be better able to apply it (even to problem domains different then the one chosen for the example). Unfortunately, the authors of this text clearly do not understand this basic aspect of human learning.
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Summary: Useful and well-written
Review: This is one of those books you keep forever, purely for its utility: it's packed with formulas, techniques, examples. But more than that, the authors lead you through the techniques and explain the concepts behind them, with the goal of equipping you with the mental tools to attack any mathematical problem you encounter. And to top it off, it's well-written, and the "margin notes" provide some comic relief. The material is very dense, and it's not a book I'd recommend for casual reading: this is stuff you only work through if you're going to need it. But if you *are* going to need it, this book will make it a lot more pleasant.
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