Main Content

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

Guest Posts

Math and Baking: Torus-Knotted Baklava

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5 thoughts on “Main Content

  1. Pingback: Cryptanalysis with N-Grams | Math ∩ Programming

  2. Pingback: Matemática e Álgebra Computacional - Márcio Francisco Dutra e Campos

  3. Pingback: The Universal Properties of Map, Fold, and Filter | Math ∩ Programming

  4. Pingback: Introducing Categories | Math ∩ Programming

  5. Pingback: Introducing Elliptic Curves | Math ∩ Programming

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