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Description
Introduction to the mathematics that supports advanced computer programming and the analysis of algorithms. An indispensable text and reference not only for computer scientists -- the authors themselves rely heavily upon it -- but for serious users of mathematics in virtually every discipline.... read more
Summary
This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums,... read more (warning: may contain spoilers)
Memorable Quotes
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“It is to be hoped that this book succeeds in convincing many educators, not only in computer science but also in mathematics, that courses like this pay off!”
J. H. Van Lint, International Reviews on Education -
“It is always a pleasure to look again into this book full of carefully explained and enthusiastically presented mathematics.”
Volker Strehl, Mathematical Reviews
First Sentence
This book is based on a course of the same name that has been taught annually at Stanford University since 1970.
Table of Contents
1.0 Recurrent Problem
1.1 The Tower of Hanoi
1.2 Lines in the Plane
1.3 The Josephus Problem
2.0 Sums
2.1 Notation
2.2 Sums and Recurrences
2.3 Manipulation of Sums
2.4 Multiple Sums
2.5 General Methods
2.6 Finite and In nite Calculus
2.7 In nite Sums
3.0 Integer Functions
3.1 Floors and Ceilings
3.2 Floor/Ceiling Applications
3.3 Floor/Ceiling Recurrences
3.4 'mod': The Binary Operation
3.5 Floor/Ceiling Sums
4.0 Number Theory
4.1 Divisibility
4.2 Primes
4.3 Prime Examples
4.4 Factorial Factors
4.5 Relative Primality
4.6 'mod': The Congruence Relation
4.7 Independent Residues
4.8 Additional Applications
4.9 Phi and Mu
5.0 Binomial Coefficients
5.1 Basic Identities
5.2 Basic Practice
5.3 Tricks of the Trade
5.4 Generating Functions
5.5 Hypergeometric Functions
5.6 Hypergeometric Transformations
5.7 Partial Hypergeometric Sums
5.8 Mechanical Summation
6.0 Special Numbers
6.1 Stirling Numbers
6.2 Eulerian Numbers
6.3 Harmonic Numbers
6.4 Harmonic Summation
6.5 Bernoulli Numbers
6.6 Fibonacci Numbers
6.7 Continuants
7.0 Generating Functions
7.1 Domino Theory and Change
7.2 Basic Maneuvers
7.3 Solving Recurrences
7.4 Special Generating Functions
7.5 Convolutions
7.6 Exponential Generating Functions
7.7 Dirichlet Generating Functions
8.0 Discrete Probability
8.1 Denitions
8.2 Mean and Variance
8.3 Probability Generating Functions
8.4 Flipping Coins
8.5 Hashing
9.0 Asymptotics
9.1 A Hierarchy
9.2 O Notation
9.3 O Manipulation
9.4 Two Asymptotic Tricks
9.5 Euler's Summation Formula
9.6 Final Summations
A Answers to Exercises
B Bibliography
C Credits for Exercises
Index
List of Tables
Errata
http://www-cs-faculty.stanford.edu/~uno/gkp.html
Authors & Contributors
- Ronald Graham (Author)
- Donald E. Knuth (Author)
- Oren Patashnik (Author)
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