Book:Donald E. Knuth/The Art of Computer Programming: Volume 2: Seminumerical Algorithms

Subject Matter

 * Number Theory
 * Discrete Mathematics
 * Computer Science

Contents

 * Preface


 * Notes on the Exercises


 * Chapter 3 - Random Numbers


 * 3.1. Introduction
 * 3.2. Generating Uniform Random Numbers
 * 3.2.1. The Linear Congruential Method
 * 3.2.1.1. Choice of modulus
 * 3.2.1.2. Choice of multiplier
 * 3.2.1.3. Potency
 * 3.2.2. Other Methods
 * 3.3. Statistical Tests
 * 3.3.1. General Test Procedures for Studying Random Data
 * 3.3.2. Empirical Tests
 * *3.3.3. Theoretical Tests
 * 3.3.4. The Spectral Test
 * 3.4. Other Types of Random Quantities
 * 3.4.1. Numerical Distributions
 * 3.4.2. Random Sampling and Shuffling
 * *3.5. What ls a Random Sequence?
 * 3.6 Summary


 * Chapter 4 - Arithmetic


 * 4.1. Positional Number Systems
 * 4.2. Floating Point Arithmetic
 * 4.2.1. Single-Precision Calculations
 * 4.2.2. Accuracy of Floating Point Arithmetic
 * *4.2.3. Double-Precision Calculations
 * 4.2.4. Distribution of Floating Point Numbers
 * 4.3. Multiple Precision Arithmetic
 * 4.3.1. The Classical Algorithms
 * *4.3.2. Modular Arithmetic
 * *4.3.3. How Fast Can We Multiply?
 * 4.4. Radix Conversion
 * 4.5. Rational Arithmetic
 * 4.5.1. Fractions
 * 4.5.2. The Greatest Common Divisor
 * *4.5.3. Analysis of Euclid's Algorithm
 * 4.5.4. Factoring into Primes
 * 4.6. Polynomial Arithmetic
 * 4.6.1. Division of Polynomials
 * *4.6.2. Factorisation of Polynomials
 * 4.6.3. Evaluation of Powers
 * 4.6.4. Evaluation of Polynomials
 * *4.7. Manipulation of Power Series


 * Answers to Exercises


 * Appendix A - Tables of Numerical Quantities
 * 1. Fundamental Constants (decimal)
 * 2. Fundamental Constants (octal)
 * 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers


 * Appendix B - Index to Notations


 * Index and Glossary