## Concrete Mathematics by Knuth: A Comprehensive Guide

If you are looking for a book that covers the foundations of mathematics for computer science, you might want to check out Concrete Mathematics by Ronald Graham, Donald Knuth, and Oren Patashnik. This book, first published in 1989, is a classic text that is widely used in computer science departments as a substantive but light-hearted treatment of the analysis of algorithms[^2^].

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In this article, we will give you an overview of what Concrete Mathematics is about, what topics it covers, and why it is a valuable resource for anyone interested in learning more about discrete mathematics, combinatorics, number theory, and other related fields. We will also show you where you can find a free PDF version of the book online.

## What is Concrete Mathematics?

The term concrete mathematics was coined by Knuth to describe a style of mathematics that is both concrete (dealing with specific objects and problems) and abstract (using general methods and principles). The book aims to teach the reader how to solve various kinds of mathematical problems that arise in computer science, such as recurrence relations, generating functions, binomial coefficients, asymptotic notation, modular arithmetic, and more.

The book is divided into 13 chapters, each focusing on a different topic. The chapters are:

Recurrences

Sums

Integer Functions

Number Theory

Binomial Coefficients

Special Numbers

Generating Functions

Discrete Probability

Asymptotics

RSA Cryptosystem (Appendix A)

Fibonacci Numbers (Appendix B)

Finite Calculus (Appendix C)

Miscellaneous Problems (Appendix D)

The book is written in a lively and informal style, with many examples, exercises, jokes, historical notes, and references. The authors also use a variety of notation and symbols to make the text more readable and expressive. For instance, they use the Greek letter sigma (â) to denote summation, the factorial sign (!) to denote product, and the floor function ([x]) to denote the greatest integer less than or equal to x.

## Why Read Concrete Mathematics?

There are many reasons why Concrete Mathematics is a worthwhile book to read for anyone interested in mathematics and computer science. Here are some of them:

The book covers a wide range of topics that are essential for understanding the theory and practice of algorithms, data structures, cryptography, complexity analysis, and more.

The book teaches the reader how to think mathematically and creatively, how to manipulate symbols and formulas, how to prove theorems and solve problems, and how to apply mathematical tools to real-world situations.

The book is fun and engaging, with many humorous anecdotes, historical facts, puzzles, challenges, and surprises. The authors also encourage the reader to explore further topics and questions on their own.

The book is accessible and self-contained, requiring only a basic knowledge of high school algebra and calculus. The authors also provide hints and solutions t