Google’s Page Rank

An Introduction, and Search Engines
A First Attempt, Mathematical Preliminaries
The Final Product
Why It Doesn’t Work Anymore

Conway’s Game of Life

The Wild World of Cellular Automata
Turing Machines and Conway’s Dreams
Conway’s Game of Life in Conway’s Game of Life

Art, Design, and Procedural Generation

Designing Non-repeating Patterns with Prime Numbers
Low-Complexity Art
Random Psychedelic Art
The Cellular Automaton Method for Procedural Cave Generation
Bezier Curves and Picasso

Language

Metrics on Words
Word Segmentation, or Makingsenseofthis
Cryptanalysis with N-Grams

Signal Processing

The Fast Fourier Transform Algorithm, and Denoising a Sound Clip

Machine Learning and Data Mining

Introduction
K-Nearest-Neighbors and Handwritten Digit Classification
The Perceptron, and All the Things it Can’t Perceive
Decision Trees and Political Party Classification
Neural Networks and the Backpropagation Algorithm
K-Means Clustering and Birth Rates

Algorithms on Graphs

Trees and Tree Traversal
Breadth-First and Depth-First Search

Computational Category Theory

A Sample of Standard ML (and a Preview of Monoids)
Categories, What’s the Point?
Introducing Categories
Categories as Types
Properties of Morphisms
Universal Properties

Computational Topology

Computing Homology

Games

Optimally Stacking the Deck: Kicsi Poker
Optimally Stacking the Deck: Texas Hold ‘Em

Graphics

Seam-carving for Content-Aware Image Scaling

Miscellaneous

Hunting Serial Killers
Eigenfaces, for Facial Recognition
Encryption & RSA
Holidays and Homicide
Numerical Integration
Busy Beavers, and the Quest for Big Numbers
Row Reduction over a Field
Complete Sequences and Magic Tricks
Well Orderings and Search

Education

Teaching Mathematics – Graph Theory
Learning Programming – Finger-Painting and Killing Zombies
How to Take a Calculus Test
Why There’s no Hitchhiker’s Guide to Mathematics

Chai – Designing a Programming Language (On Hold Pending Original Ideas)

Introduction
The Most Basic Interpreter (numbers and sums)
Arithmetic and Organization (arithmetic, boolean algebra)
Environments and Variables (“with” and “ref”)
Functions and Function Applications (“fun”, “app”, “if”, and pairs)