Mathematics for ML
Vectors and dot products, matrices as transformations, eigenvectors, SVD and PCA, calculus and gradients, probability, likelihood and information theory.
6 animated lectures · 66 minutes
▶ Start with lecture 1Vectors, Norms and the Dot Product
A deep dive into the object every model is built from: what vectors are, how to add, scale and measure them, and why the dot product powers neurons, attention and semantic search.
Matrices as Transformations
See matrices as machines that transform space: matrix–vector products, composition, determinants, inverses and rank — and why every neural-network layer is a matrix.
Eigenvectors, SVD and PCA
Find the directions a matrix does not turn, break any matrix into rotate–stretch–rotate, and use it to compress data with principal component analysis.
Calculus for Machine Learning: Derivatives, Gradients and the Chain Rule
How models learn by following slopes: derivatives, partial derivatives, gradients, gradient descent, saddle points and the chain rule that makes backpropagation possible.
Probability and Distributions for ML
Random variables, expectation and variance, the Bernoulli, binomial and normal distributions, the central limit theorem, Monte Carlo methods and Markov chains — with live simulations.
Likelihood, Bayes and Information Theory
Why models minimise cross-entropy: maximum likelihood, priors and MAP, Bayesian updating, entropy, cross-entropy and KL divergence — the statistics hiding inside every loss function.