Concrete Mathematics

Ronald L. Graham (1935-2020) was the Chief Scientist at AT&T Labs Research for many years. He was also a former President of the American Mathematical Society and the Mathematical Association of America, as well as a Professor of Computer and Information Science at the University of California, San Diego.

Donald E. Knuth is Stanford University's Emeritus Professor of The Art of Computer Programming. He wrote four books on The Art of Computer Programming and five books about his TEX and METAFONT typesetting technologies.

Oren Patashnik works as a researcher at the Center for Communications Research in La Jolla, California. He is also the creator of BibTEX, a popular bibliography processor.

Concrete Mathematics introduces the mathematics that underpins advanced computer programming and algorithm analysis. The fundamental goal of its well-known writers is to establish a robust and useful foundation of mathematical skills - the skills required to solve complex problems, evaluate astronomical amounts, and identify subtle patterns in data. It is a must-have work and reference not only for computer scientists (the authors rely extensively on it! ), but also for serious users of mathematics in almost every discipline.

CONtinuous and disCRETE mathematics are combined in Concrete Mathematics. "More concretely," the authors add, "it is the controlled manipulation of mathematical formulas, employing a set of problem-solving approaches." The subject content is mainly an elaboration of Knuth's famous Art of Computer Programming's Mathematical Preliminaries part, although the presenting manner is more leisurely, and individual topics are addressed more thoroughly. A number of new themes have been introduced, and the most important ideas have been traced back to their historical origins. The book has around 500 activities grouped into six categories. All exercises, with the exception of research problems, provide complete answers, making the book especially useful for self-study.

Major topics include:

• Sums
• Recurrences
• Integer functions
• Elementary number theory
• Binomial coefficients
• Generating functions
• Discrete probability
• Asymptotic methods

This second edition contains significant new material on mechanical summation. In response to the original edition's broad use as a reference book, the bibliography and index have been increased, and nontrivial enhancements can be found on practically every page. Concrete Mathematics' conversational approach will appeal to readers. The marginal graffiti created by students who have attended courses based on this subject is really enjoyable. The writers hope to convey not only the relevance of the skills given, but also some of the enjoyment in learning and applying them.

Author: Ronald L. Graham, Donald E. Knuth and Oren Patashnik

Link to buy: https://www.amazon.com/Concrete-Mathematics-Foundation-Computer-Science/dp/0201558025/

Ratings: 4.6 out of 5 stars (from 183 reviews)

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