第2卷对半数值算法领域做了全面介绍，分“随机数”和“算术”两章。本卷总结了主要算法范例及这些算法的基本理论，广泛剖析了计算机程序设计与数值分析间的相互联系。第3版中*引人注目的是，Knuth对随机数生成器进行了重新处理，对形式幂级数计算作了深入讨论。
本书是国内外业广泛关注的《计算机程序设计艺术》的第3 卷。本卷首先介绍编程的基本概念和技术，然后详细讲解信息结构方面的内容，包括信息在计算机内部的表示方法、数据元素之间的结构关系等方面的初级应用。

Chapter 1 Basic Concepts
1.1. Algorithms
1.2. Mathematical Preliminaries
1.2.1. Mathematical Induction
1.2.2. Numbers, Powers, and Logarithms
1.2.3. Sums and Products
1.2.4. Integer Functions and Elementary Number Theory
1.2.5. Permutations and Factorials
1.2.6. Binomial Coefficients
1.2.7. Harmonic Numbers
1.2.8. Fibonacci Numbers
1.2.9. Generating Functions
1.2.10. Analysis of an Algorithm
*1.2.11. Asymptotic Representations
*1.2.11.1. The O-notation
*1.2.11.2. Euler's summation formula
*1.2.11.3. Some asymptotic calculations
1.3. MIX 124
1.3.1. Description of MIX
1.3.2. The MIX Assembly Language
1.3.3. Applications to Permutations
1.4. Some Fundamental Programming Techniques
1.4.1. Subroutines
1.4.2. Goroutines
1.4.3. Interpretive Routines
1.4.3.1. A MIX simulator
*1.4.3.2. Trace routines
1.4.4. Input and Output
1.4.5. History and Bibliography

Chapter 2 Information Structures
2.1. Introduction
2.2. Linear Lists
2.2.1. Stacks, Queues, and Deques
2.2.2. Sequential Allocation
2.2.3. Linked Allocation
2.2.4. Circular Lists
2.2.5. Doubly Linked Lists
2 2.6. Arrays and Orthogonal Lists
2.3. Trees
2.3.1. Traversing Binary Trees
2.3.2. Binary Tree Representation of Trees
2.3.3. Other Representations of Trees
2.3.4. Basic Mathematical Properties of Trees
2.3.4.1. Free trees
2.3.4.2. Oriented trees
*2.3.4.3. The "infinity lemma"
*2.3.4.4. Enumeration of trees
2.3.4.5. Path length
*2.3.4.6. History and bibliography
2.3.5. Lists and Garbage Collection
2.4. Multilinked Structures
2.5. Dynamic Storage Allocation
History and Bibliography
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
Excerpt

Chapter 3 Random Numbers.
Introduction.
Generating Uniform Random Numbers.
The Linear Congruential Method.
Other Methods.
Statistical Tests.
General Test Procedures for Studying Random Data.
Empirical Tests.
Theoretical Tests.
The Spectral Test.
Other Types of Random Quantities.
Numerical Distributions.
Random Sampling and Shuffling.
What Is a Random Sequence?
Summary.

Chapter 4 Arithmetic.
Positional Number Systems.
Floating Point Arithmetic.
Single-Precision Calculations.
Accuracy of Floating Point Arithmetic.
Double-Precision Calculations.
Distribution of Floating Point Numbers.
Multiple Precision Arithmetic.
The Classical Algorithms.
Modular Arithmetic.
How Fast Can We Multiply?.
Radix Conversion.
Rational Arithmetic.
Fractions.
The Greatest Common Divisor.
Analysis of Euclid's Algorithm.
Factoring into Primes.
Polynomial Arithmetic.
Division of Polynomials.
Factorization of Polynomials.
Evaluation of Powers.
Evaluation of Polynomials.
Manipulation of Power Series.
Answers to Exercises.

Appendix A: Tables of Numerical Quantities.
Fundamental Constants (decimal).
Fundamental Constants (octal).
Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers.

Appendix B: Index to Notations.
Index and Glossary.

Chapter 5 Sorting.
Combinatorial Properties of Permutations.
Inversions.
Permutations of a Multiset.
Runs.
Tableaux and Involutions.
Internal sorting.
Sorting by Insertion.
Sorting by Exchanging.
Sorting by Selection.
Sorting by Merging.
Sorting by Distribution.
Optimum Sorting.
Minimum-Comparison Sorting.
Minimum-Comparison Merging.
Minimum-Comparison Selection.
Networks for Sorting.
External Sorting.
Multiway Merging and Replacement Selection.
The Polyphase Merge.
The Cascade Merge.
Reading Tape Backwards.
The Oscillating Sort.
Practical Considerations for Tape Merging.
External Radix Sorting.
Two-Tape Sorting.
Disks and Drums.
Summary, History, and Bibliography.

Chapter 6 Searching.
Sequential Searching.
Searching by Comparison of Keys.
Searching an Ordered Table.
Binary Tree Searching.
Balanced Trees.
Multiway Trees.
Digital Searching.
Hashing.
Retrieval on Secondary Keys.
Answers to Exercises.

Appendix A: Tables of Numerical Quantities.
Fundamental Constants (decimal).
Fundamental Constants (octal).
Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers.

Appendix B:Index to Notations.
Index and Glossary.

为反映计算机领域的*新发展，Knuth二十多年来**次将三卷书全部做了修订。他的修订主要集中在自上一版以来得到众人认可的新知识，已经解决的问题，以及有所变化的问题。为保持本书的权威性，在必要的地方对计算机领域先驱工作的历史信息做了更新；为维护作者苦心孤诣追求至善至美的盛誉，新版本对读者发现的少量技术性错误做了更正；为增加本书的挑战性，作者还添加了数百道习题。本套书由3卷组成。