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
        • 2.2.3. 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
      • 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?
      • 4.4. 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. 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
        • 5.4.3. The Cascade Merge
        • 5.4.4. Reading Tape Backwards
        • 5.4.5. The Oscillating Sort
        • 5.4.6. Practical Considerations for Tape Merging
        • 5.4.7. External Radix Sorting
        • 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

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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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