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Art, Graphics, and Procedural Generation
Designing Non-repeating Patterns with Prime Numbers
Low-Complexity ArtRandom Psychedelic Art
Seam-carving for Content-Aware Image Scaling
The Cellular Automaton Method for Procedural Cave Generation
Bezier Curves and Picasso
Making Hybrid Images
Low-Complexity ArtRandom Psychedelic Art
Seam-carving for Content-Aware Image Scaling
The Cellular Automaton Method for Procedural Cave Generation
Bezier Curves and Picasso
Making Hybrid Images
Signal Processing
The Fast Fourier Transform Algorithm, and Denoising a Sound Clip
The Two-Dimensional Fourier Transform and Digital Watermarking
Making Hybrid Images
The Welch-Berlekamp Algorithm for Correcting Errors in Data
The Two-Dimensional Fourier Transform and Digital Watermarking
Making Hybrid Images
The Welch-Berlekamp Algorithm for Correcting Errors in Data
Machine Learning and Data Mining
Introduction
K-Nearest-Neighbors and Handwritten Digit ClassificationThe 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 (via Principal Component Analysis)
Bandit Learning: the UCB1 Algorithm
Bandit Learning: the EXP3 Algorithm
Bandits and Stocks
Weak Learning, Boosting, and the AdaBoost Algorithm
Fairness in machine learning (introduction, statistical parity)
The Johnson-Lindenstrauss Transform
Singular Value Decomposition (motivation, algorithms)
Support Vector Machines (inner products, primal problem, dual problem)
K-Nearest-Neighbors and Handwritten Digit ClassificationThe 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 (via Principal Component Analysis)
Bandit Learning: the UCB1 Algorithm
Bandit Learning: the EXP3 Algorithm
Bandits and Stocks
Weak Learning, Boosting, and the AdaBoost Algorithm
Fairness in machine learning (introduction, statistical parity)
The Johnson-Lindenstrauss Transform
Singular Value Decomposition (motivation, algorithms)
Support Vector Machines (inner products, primal problem, dual problem)
Graphs and Network Science
Binary Search on Graphs
Trees and Tree Traversal
Breadth-First and Depth-First Search
The Erdős-Rényi Random Graph
The Giant Component and Explosive Percolation
Zero-One Laws for Random Graphs
Community Detection in Graphs, a Casual Tour
Google’s PageRank Algorithm:
Introduction,
A First Attempt,
The Final Product,
Why It Doesn’t Work Anymore
Trees and Tree Traversal
Breadth-First and Depth-First Search
The Erdős-Rényi Random Graph
The Giant Component and Explosive Percolation
Zero-One Laws for Random Graphs
Community Detection in Graphs, a Casual Tour
Google’s PageRank Algorithm:
Introduction,
A First Attempt,
The Final Product,
Why It Doesn’t Work Anymore
Combinatorial Optimization
When Greedy is Good Enough: Submodularity and the 1 – 1/e ApproximationWhen Greedy Algorithms are Perfect: the Matroid
Linear Programming and Healthy Diets Part 1
Linear Programming and the Simplex Algorithm
Linear Programming and Healthy Diets Part 2
The Many Faces of Set Cover
Linear Programming and Healthy Diets Part 1
Linear Programming and the Simplex Algorithm
Linear Programming and Healthy Diets Part 2
The Many Faces of Set Cover
Algorithmic Game Theory
Quantum Computing
A Motivation for Quantum Computing
The Quantum Bit
Multiple Qubits and the Quantum Circuit
Concrete Examples of Quantum Gates
The Quantum Bit
Multiple Qubits and the Quantum Circuit
Concrete Examples of Quantum Gates
Cryptography
RSAElliptic Curves IntroductionElliptic 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)
The Mathematics of Secret Sharing
Zero Knowledge Proofs (primer, zero knowledge proofs for NP, definitions and theory)
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)
The Mathematics of Secret Sharing
Zero Knowledge Proofs (primer, zero knowledge proofs for NP, definitions and theory)
Streaming and Sublinear Algorithms
Natural Language
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
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
Games
The Wild World of Cellular Automata
Turing Machines and Conway’s DreamsConway’s Game of Life in Conway’s Game of Life
Optimally Stacking the Deck: Kicsi PokerOptimally Stacking the Deck: Texas Hold ‘EmWant to make a great puzzle game? Get inspired by theoretical computer science.
Turing Machines and Conway’s DreamsConway’s Game of Life in Conway’s Game of Life
Optimally Stacking the Deck: Kicsi PokerOptimally Stacking the Deck: Texas Hold ‘EmWant to make a great puzzle game? Get inspired by theoretical computer science.
Miscellaneous
The Reasonable Effectiveness of the Multiplicative Weights Update Algorithm
Hunting Serial Killers
Learning to Love Complex Numbers
Holidays and Homicide
Numerical Integration
Busy Beavers, and the Quest for Big NumbersRow Reduction over a Field
Complete Sequences and Magic Tricks
Well Orderings and Search
Hunting Serial Killers
Learning to Love Complex Numbers
Holidays and Homicide
Numerical Integration
Busy Beavers, and the Quest for Big NumbersRow 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
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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