Concrete MathematicsA Foundation for Computer Science
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(Most chapters contain Exercises.)
1. Recurrent Problems.
The Tower of Hanoi.Lines in the Plane.The Josephus Problem.Exercises.
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.
A Hierarchy.O Notation.O Manipulation.Two Asymptotic Tricks.Euler's Summation Formula.Final Summations.Exercises.
A. Answers to Exercises.
C. Credits for Exercises.
List of Tables. 0201558025T04062001
Donald E. Knuth is known throughout the world for his pioneering work on algorithms and programming techniques, for his invention of the Tex and Metafont systems for computer typesetting, and for his prolific and influential writing. Professor Emeritus of The Art of Computer Programming at Stanford University, he currently devotes full time to the completion of these fascicles and the seven volumes to which they belong.