Supplementary materials
Statistics
- Visualizing the multivariate normal distribution
- Visualizing KL-divergence
- Bayes’ Theorem: The Geometry of Changing Beliefs. YouTube video @3Blue1Brown channel.
Optimization
- Gradient descent visualizer (Interactive web app.)
- Gradient descent visualization (MacOS/Windows app.) Note: The Github page includes some animated images, but the app needs to be installed on your computer to use interactively. Do so at your own risk! (The app is distributed by an independent academic researcher/programmer, not by a software company.)
Overfitting and underfitting (bias and variance)
Regions, Surfaces and Curves
- CalcPlot3D: A web app to plot curves, surfaces and regions in 3D-space described in various representations (explicit, implicit, parametric, inequalities, etc.).
- Parametric Curve Grapher
Derivatives and gradients
- Web applet: Gradient and directional derivative on a mountain hosted at MathInsights.org. (Students are encouraged to look at the many other applets illustrating concepts —primarily in calculus.)
- Just for fun! AI-generated (Gemini) video illustrating gradient flow on a surface.