Concrete Mathematics

(Most chapters contain Exercises.)

1. Recurrent Problems.
The Tower of Hanoi.Lines in the Plane.The Josephus Problem.Exercises.

2. Sums.
Notation.Sums and Recurrences.Manipulation of Sums.Multiple Sums.General Methods.Finite and Infinite Calculus.Infinite Sums.Exercises.

3. Integer Functions.
Floors and Ceilings.Floor/Ceiling Applications.Floor/Ceiling Recurrences.'mod': The Binary Operation.Floor/Ceiling Sums.Exercises.

4. Number Theory.
Divisibility.Factorial Factors.Relative Primality.'mod': The Congruence Relation.Independent Residues.Additional Applications.Phi and Mu.Exercises.

5. Binomial Coefficients.
Basic Identities.Basic Practice.Tricks of the Trade.Generating Functions.Hypergeometric Functions.Hypergeometric Transformations.Partial Hypergeometric Sums.Mechanical Summation.Exercises.

6. Special Numbers.
Stirling Numbers.Eulerian Numbers.Harmonic Numbers.Harmonic Summation.Bernoulli Numbers.Fibonacci Numbers.Continuants.Exercises.

7. Generating Functions.
Domino Theory and Change.Basic Maneuvers.Solving Recurrences.Special Generating Functions.Convolutions.Exponential Generating Functions.Dirichlet Generating Functions.Exercises.

8. Discrete Probability.
Definitions.Mean and Variance.Probability Generating Functions.Flipping Coins.Hashing.Exercises.

9. Asymptotics.
A Hierarchy.O Notation.O Manipulation.Two Asymptotic Tricks.Euler's Summation Formula.Final Summations.Exercises.

A. Answers to Exercises.


B. Bibliography.


C. Credits for Exercises.


Index.


List of Tables. 0201558025T04062001