Foundations
Short interactive companions to One Concept, One Example videos.
Watch one idea, manipulate one example, and leave with intuition. Each module takes about 5–8 minutes.
01Statistical Toolkit
Probability, inference, uncertainty, and statistical reasoning through focused examples.
14 modules+
Statistical Toolkit
Probability, inference, uncertainty, and statistical reasoning through focused examples.
- 01
Random Variables
One Concept · One Example
- 02
Marginal and Conditional Distributions
One Concept · One Example
- 03
Gaussian Distributions
One Concept · One Example
- 04
Moments and Non-Gaussian Distributions
One Concept · One Example
- 05
Gaussian Mixture Distributions
One Concept · One Example
- 06
Bayes Theorem
One Concept · One Example
- 07
The Monte Carlo Method: Core Idea
One Concept · One Example
- 08
The Monte Carlo Method: Mathematical Definition
One Concept · One Example
- 09
Markov Chain Monte Carlo: The Metropolis Algorithm
One Concept · One Example
- 10
Markov Chain Monte Carlo: Reconstructing Distributions
One Concept · One Example
- 11
Markov Chain Monte Carlo: Parameter Estimation
One Concept · One Example
- 12
Importance Sampling for Integration
One Concept · One Example
- 13
Importance Sampling for Rare Events
One Concept · One Example
- 14
Simulated Annealing
One Concept · One Example
02Machine Learning Toolkit
Core machine-learning ideas, from dimension reduction and clustering to neural networks.
18 modules+
Machine Learning Toolkit
Core machine-learning ideas, from dimension reduction and clustering to neural networks.
- 01
Principal Component Analysis: Motivation
One Concept · One Example
- 02
Principal Component Analysis: Definition
One Concept · One Example
- 03
K-Means: A Canonical Clustering Method
One Concept · One Example
- 04
Determining the Number of Clusters
One Concept · One Example
- 05
K-Means in High Dimensions
One Concept · One Example
- 06
Fuzzy Clustering
One Concept · One Example
- 07
Logistic Regression
One Concept · One Example
- 08
K-Nearest Neighbors
One Concept · One Example
- 09
Linear Regression
One Concept · One Example
- 10
PCA and Linear Regression
One Concept · One Example
- 11
Gaussian Process Regression
One Concept · One Example
- 12
Neural Networks: Basic Architecture
One Concept · One Example
- 13
Combining Neurons into a Network
One Concept · One Example
- 14
Training a Neural Network
One Concept · One Example
- 15
The Role of Weights and Biases
One Concept · One Example
- 16
Nonlinear Activation Functions
One Concept · One Example
- 17
Transfer Learning with Limited Data
One Concept · One Example
- 18
Entropy-Constrained Learning
One Concept · One Example
03Dynamical Toolkit
Stability, oscillations, feedbacks, bifurcations, chaos, numerical methods, and wave dynamics.
15 modules+
Dynamical Toolkit
Stability, oscillations, feedbacks, bifurcations, chaos, numerical methods, and wave dynamics.
- 01
Ordinary Differential Equations: Introduction
One Concept · One Example
Video coming soonExplore companion → - 02
General First-Order Linear ODEs
One Concept · One Example
Video coming soonExplore companion → - 03
Damping, Forcing, and Equilibrium
One Concept · One Example
Video coming soonExplore companion → - 04
From Higher-Order ODEs to First-Order Systems
One Concept · One Example
Video coming soonExplore companion → - 05
Simple Nonlinear ODEs
One Concept · One Example
Video coming soonExplore companion → - 06
Saddle-Node Bifurcation
One Concept · One Example
Video coming soonExplore companion → - 07
Transcritical and Pitchfork Bifurcations
One Concept · One Example
Video coming soonExplore companion → - 08
Chaotic Systems
One Concept · One Example
Video coming soonExplore companion → - 09
The Lorenz 63 Model
One Concept · One Example
Video coming soonExplore companion → - 10
Forward Euler Method
One Concept · One Example
Video coming soonExplore companion → - 11
Instability in Stiff Systems
One Concept · One Example
Video coming soonExplore companion → - 12
Higher-Order Numerical Methods
One Concept · One Example
Video coming soonExplore companion → - 13
Introduction to Partial Differential Equations
One Concept · One Example
Video coming soonExplore companion → - 14
Wave Mode Analysis
One Concept · One Example
Video coming soonExplore companion → - 15
Wave Modes of the Shallow Water Equations
One Concept · One Example
Video coming soonExplore companion →
04Applied Analysis Toolkit
Approximation, scale, asymptotics, operators, and analytical reasoning for complex systems.
Coming soon+
Applied Analysis Toolkit
Approximation, scale, asymptotics, operators, and analytical reasoning for complex systems.
05Stochastic Toolkit
Random processes, stochastic differential equations, noise, memory, and uncertainty.
Coming soon+
Stochastic Toolkit
Random processes, stochastic differential equations, noise, memory, and uncertainty.