# The Art of Computer Programming - Volumes - Chapter Outline of Published Volumes

Chapter Outline of Published Volumes

• Volume 1 – Fundamental Algorithms
• 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 MMIX (MIX in the hardback copy but updated by fascicle 1)
• 1.3.1. Description of MMIX
• 1.3.2. The MMIX Assembly Language
• 1.3.3. Applications to Permutations
• 1.4. Some Fundamental Programming Techniques
• 1.4.1. Subroutines
• 1.4.2. Coroutines
• 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
• 2.2.4. Circular 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
• 2.5. Dynamic Storage Allocation
• 2.6. History and Bibliography
• Volume 2 – Seminumerical Algorithms
• 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 Is 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?
• 4.5. 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. Factorization of Polynomials
• 4.6.3. Evaluation of Powers
• 4.6.4. Evaluation of Polynomials
• 4.7. Manipulation of Power Series
• Volume 3 – Sorting and Searching
• Chapter 5 – Sorting
• 5.1. Combinatorial Properties of Permutations
• 5.1.1. Inversions
• 5.1.2. Permutations of a Multiset
• 5.1.3. Runs
• 5.1.4. Tableux and Involutions
• 5.2. Internal sorting
• 5.2.1. Sorting by Insertion
• 5.2.2. Sorting by Exchanging
• 5.2.3. Sorting by Selection
• 5.2.4. Sorting by Merging
• 5.2.5. Sorting by Distribution
• 5.3. Optimum Sorting
• 5.3.1. Minimum-Comparison Sorting
• 5.3.2. Minimum-Comparison Merging
• 5.3.3. Minimum-Comparison Selection
• 5.3.4. Networks for Sorting
• 5.4. External Sorting
• 5.4.1. Multiway Merging and Replacement Selection
• 5.4.2. The Polyphase Merge
• 5.4.5. The Oscillating Sort
• 5.4.6. Practical Considerations for Tape Merging
• 5.4.8. Two-Tape Sorting
• 5.4.9. Disks and Drums
• 5.5. Summary, History, and Bibliography
• Chapter 6 – Searching
• 6.1. Sequential Searching
• 6.2. Searching by Comparison of Keys
• 6.2.1. Searching an Ordered Table
• 6.2.2. Binary Tree Searching
• 6.2.3. Balanced Trees
• 6.2.4. Multiway Trees
• 6.3. Digital Searching
• 6.4. Hashing
• 6.5. Retrieval on Secondary Keys
• Volume 4A – Combinatorial Algorithms, Part 1
• Chapter 7 – Combinatorial Searching
• 7.1. Zeros and Ones
• 7.1.1. Boolean Basics
• 7.1.2. Boolean Evaluation
• 7.1.3. Bitwise Tricks and Techniques
• 7.1.4. Binary Decision Diagrams
• 7.2. Generating All Possibilities
• 7.2.1. Generating Basic Combinatorial Patterns
• 7.2.1.1. Generating all n-tuples
• 7.2.1.2. Generating all permutations
• 7.2.1.3. Generating all combinations
• 7.2.1.4. Generating all partitions
• 7.2.1.5. Generating all set partitions
• 7.2.1.6. Generating all trees
• 7.2.1.7. History and further references

### Other articles related to "chapter outline of published volumes, volume, chapter":

The Art Of Computer Programming - Volumes - Chapter Outline of Published Volumes
... Volume 1 – Fundamental Algorithms Chapter 1 – Basic concepts 1.1 ... History and Bibliography Chapter 2 – Information Structures 2.1 ... History and Bibliography Volume 2 – Seminumerical Algorithms Chapter 3 – Random Numbers 3.1 ...

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