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Concrete_Mathematics_2nd_Ed_TeX_Source_Code

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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\dash---the skills
needed to solve complex problems, to evaluate horrendous sums, and to
discover subtle patterns in data. It is an indispensible text and
reference not only for computer scientists\dash---the authors themselves
rely heavily on it!\dash---but for serious users of mathematics in
virtually every discipline.

Concrete mathematics is a blending of {\sc con}tinuous and dis{\sc crete}
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 {\sl 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.

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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 {\sl Concrete Mathematics}.
Particularly enjoyable are the marginal graffiti contributed by
students who have taken courses based on this material. Graham, Knuth,
and Patashnik want to convey not only the importance of the techniques
presented, but some of the fun in learning and using them.

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{\subsubtitle\kern-.5pt About the authors:}\hfill\break
{\sc Ronald L. Graham} is Adjunct Director for Research in the
Information Science Division of AT\&T Bell Laboratories. He is also
University Professor of Mathematical Sciences at Rutgers University.
\kern1ptDr.\thinspace Graham is the author of five other mathematics books.

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{\sc Donald E. Knuth} is Professor Emeritus of The Art of Computer Programming
at Stanford University. His prolific writings include three volumes
on the {\sl Art of Computer Programming}, and five books related
to his \TeX\ and \MF\ typesetting systems.

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{\sc Oren Patashnik} is a member of the research staff at the Center for
Communications Research, La Jolla. He is also the author of Bib\-\TeX,
a widely used bibliography processor.


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