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 areference 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
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