# Jon Aquino's Mental Garden

 Engineering beautiful software jon aquino labs | personal blog

## Saturday, April 10, 2010

I am tempted to make another attempt at reading this stuff.

## 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
2.2.4. 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
History and Bibliography

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?.
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.

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 Oscillating Sort.
Practical Considerations for Tape Merging.
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.

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.

• Jonathan this is a bunch of gibberish to me. But I do have one question. What are Harmonic Numbers and Bernoulli Numbers? Anything as interesting and worth knowing as Fibonacci Numbers?

-Lola

By  Anonymous, at 5/05/2010 11:17 p.m.

• @Lola - Offhand I'm not sure what Bernoulli numbers are. The harmonic numbers are:

1
1 + 1/2
1 + 1/2 + 1/3
1 + 1/2 + 1/3 + 1/4
etc.