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Companion to Concrete Mathematics [Paperback]

Z. A. Melzak

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Book Description

June 25 2007 0486457818 978-0486457819 1
Many texts emphasize generality and abstract principles at the expense of concreteness; this text remedies that common mistake, stressing formal manipulations, intuitive appeal, and ingenuity. A two-volume treatment in a single binding, it supplements standard mathematics courses, employing physical analogies, encouraging problem formulation, and supplying problem-solving methods.
Since it addresses topics of varying complexity—from number-multiplication games and other recreational mathematics to the zeros of the Riemann zeta function and the presumed transcendence of Euler's constant—this volume can be used by readers of every background. Beginners will find it a source of useful techniques and subjects not usually taught in standard courses. They'll also discover connections between seemingly unrelated aspects of mathematics. Experienced mathematicians can rely upon the book as a source of problems and information on branches beyond their specialties. Other professionals—theoretical physicists and chemists, engineers, numerical analysts, and computer scientists—will also consider it a valuable reference.

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Product Details

  • Paperback: 720 pages
  • Publisher: Dover Publications; 1 edition (June 25 2007)
  • Language: English
  • ISBN-10: 0486457818
  • ISBN-13: 978-0486457819
  • Product Dimensions: 14.2 x 3.6 x 21.3 cm
  • Shipping Weight: 635 g
  • Amazon Bestsellers Rank: #512,177 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com: 2.5 out of 5 stars  2 reviews
4 of 9 people found the following review helpful
2.0 out of 5 stars Book has serious drawbacks Dec 30 2010
By A customer - Published on Amazon.com
An excellent review is published elsewhere, not by me: [...] . I will summarize it here, but you should read the complete review as it's wonderful in itself. Having read that review helped me avoid this book, so I am hoping it will be useful to others.

The author of the review above comes to the conclusion that the book has some breadth, though at the expense of depth, and the organization seems haphazard. There are serious errors and typos in the book which affect its readability. Of particularly importance is that problems are not graded on difficulty -- it's hard to tell what's a simple problem and what is an open question. The reviewer above pointed out one specific problem, which was clarified as being simply a conjecture rather than a theorem that has a known proof by the book author. Contrast this to Don Knuth's "The Art of Computer Programming" in which he meticulously graded problems so that it's easy to see what's a simple 10-minute problem, what will take an hour, and what's still an open research problem.

The book's index is far from complete and the references to multi-volume works are not precise enough to be useful (i.e., missing page numbers in a book whose total page count is over 1000). The book also seems to have missed prior work and source of where the problems have appeared, most notably in Putnam competitions.
9 of 28 people found the following review helpful
3.0 out of 5 stars Not what its advertised but is its own Aug. 7 2010
By Claire Jones - Published on Amazon.com
Format:Paperback|Verified Purchase
I purchased this book thinking it would go along with Concrete Mathematics by Graham and Knuth. That, it is not! It is valuable as a stand-a-lone source. I rated it as a 3 due to the False Advertising by the title. I would rate it as a 5 if it retitled itself. The content is very good if you are searching for advanced material on this subject.

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