Book:Ronald L. Graham/Concrete Mathematics: A Foundation for Computer Science
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Ronald L. Graham, Donald E. Knuth and Oren Patashnik: Concrete Mathematics: A Foundation for Computer Science
Published $\text {1989}$
Subject Matter
Contents
- Recurrent Problems
- The Tower of Hanoi
- Lines in the Plane
- The Josephus Problem
- Sums
- Notation
- Sums and Recurrences
- Manipulation of Sums
- Multiple Sums
- General Methods
- Finite and Infinite Calculus
- Infinite Sums
- Integer Functions
- Floors and Ceilings
- Floor / Ceiling Applications
- Floor / Ceiling Recurrences
- 'mod': The Binary Operation
- Floor / Ceiling Sums
- Number Theory
- Divisibility
- Primes
- Prime Examples
- Factorial Factors
- Relative Primality
- 'mod': The Congruence Relation
- Independent Residues
- Additional Applications
- Phi and Mu
- Binomial Coefficients
- Basic Identities
- Basic Practice
- Tricks of the Trade
- Generating Functions
- Hypergeometric Functions
- Hypergeometric Transformations
- Partial Hypergeometric Sums
- Mechanical Summation
- Special Numbers
- Stirling Numbers
- Eulerian Numbers
- Harmonic Numbers
- Harmonic Summation
- Bernoulli Numbers
- Fibonacci Numbers
- Generating Functions
- Domino Theory and Change
- Basic Maneuvers
- Solving Recurrences
- Special Generating Functions
- Convolutions
- Exponential Generating Functions
- Dirichlet Generating Functions
- Discrete Probability
- Definitions
- Mean and Variance
- Probability Generating Functions
- Flipping Coins
- Hashing
- Asymptotics
- A Hierarchy
- O Notation
- O Manipulation
- Two Asymptotic Tricks
- Euler's Summation Formula
- Final Summations