## Google’s Page Rank

An Introduction, and Search Engines

A First Attempt, Mathematical Preliminaries

The Final Product

Why It Doesn’t Work Anymore

## 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

## Signal Processing

The Fast Fourier Transform Algorithm, and Denoising a Sound Clip

The Two-Dimensional Fourier Transform and Digital Watermarking

## 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

Linear Regression

Eigenfaces, for Facial Recognition

Bandit Learning: the UCB1 Algorithm

Bandit Learning: the EXP3 Algorithm

Bandits and Stocks

## Graphs and Random Graph Models

Trees and Tree Traversal

Breadth-First and Depth-First Search

The Erdős-Rényi Random Graph

## Combinatorial Optimization

Stable Marriages and Designing Markets

## Graphics

Seam-carving for Content-Aware Image Scaling

## 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

## Cryptography

RSA

Elliptic Curves Introduction

Elliptic Curves as Elementary Equations

Elliptic Curves as Algebraic Structures

Elliptic Curves as Python Objects (over the rational numbers)

Programming with Finite Fields

Connecting Elliptic Curves with Finite Fields

Elliptic Curve Diffie-Hellman

Sending and Authenticating Messages with Elliptic Curves (Shamir-Massey-Omura and ElGamal)

## Language

Metrics on Words

Word Segmentation, or Makingsenseofthis

Cryptanalysis with N-Grams

## 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

Functoriality

The Universal Properties of Map, Fold, and Filter

## Computational Topology

Computing Homology

Fixing Bugs in Computing Homology

## Games

Optimally Stacking the Deck: Kicsi Poker

Optimally Stacking the Deck: Texas Hold ‘Em

Want to make a great puzzle game? Get inspired by theoretical computer science.

## Miscellaneous

Hunting Serial Killers

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

Deconstructing the Common Core Mathematical Standard

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