Interactive Demos

Every interactive demo on this site, gathered in one index. Each one runs entirely in your browser, inside the notes it belongs to — this page is only the map. The demos are grouped the way the site is: mathematics first, then machine learning.

Mathematics

Random Matrices

• The Semicircle Law — eigenvalues of a random symmetric matrix fill out Wigner's semicircle as the dimension grows.
• The Circular Law — eigenvalues of a non-symmetric matrix spread uniformly over a disk.
• The Marčenko–Pastur Law — the spectrum of a sample covariance matrix, against its limiting density.
• Spectra of Random Graphs — adjacency spectra as a graph is drawn edge by edge.
• Centralities — eigenvector and other centrality measures on a living network.
• Erdős–Rényi and Stochastic Block — community structure appearing in a random graph's spectrum.

Calculus 3

• Surfaces in 3D — rotatable three-dimensional plots of multivariable functions.
• Single-Variable Functions — interactive plots for limits, derivatives and integrals.

Probability & Statistics

• Random Variables — a working probability calculator: set a distribution and bounds, and read off the area.
• Hypothesis Testing — test statistics and rejection regions you can push around.

Machine Learning

Neural Networks

• Architecture Explorer — build a network layer by layer and watch the parameter count.
• A Network Learns — a hand-coded backpropagation trainer carving decision boundaries (XOR, rings, moons) in real time.
• A CNN in Your Browser — draw a digit; a convolutional network reads it.

Natural Language Processing

• The Embedding Explorer — toy word vectors: nearest neighbours by cosine similarity, and analogies by arithmetic.
• The Regex Tester — type a pattern and watch where it lands, matches highlighted with their groups.

Classification & Clustering

• The Perceptron — the original linear classifier, learning a separating line step by step.

Optimization

• Minimization in 2D and 3D — descent paths drawn over the surface they descend.

Linear Models

• Interactive Fitting — place the points yourself and fit them: least squares, regularized variants, and gradient descent.