Vectors, matrices, derivatives, probability, optimization, and stochastic calculus — from zero to the math you need to read modern ML papers. 17 lessons, foundations through advanced.
Understand vectors as geometric objects with direction and magnitude, and learn how vector spaces form the foundation of ML data representation.
See matrices as space-warping machines. Every neural network layer is a matrix multiplication — learn why that matters.
Index notation, einsum semantics, batched ops, broadcasting, and computational graphs — the language every transformer and CNN forward pass speaks.
Discover the special directions that matrices stretch without rotating, and how SVD decomposes any transformation into simple pieces.
From single-variable derivatives to multivariable gradients — the mathematical engine behind backpropagation.
Jacobian, Hessian, key matrix-calculus identities, and a full end-to-end derivation of backprop for a softmax + cross-entropy classifier.
Learn to think probabilistically. Bayes' theorem is the foundation of classification, generative models, and reasoning under uncertainty.
Mean, median, mode, standard deviation, and the distributions that appear everywhere in ML.
From random variables to expectation and variance — the statistical quantities that define every ML loss function and training process.
Joint, marginal, and conditional distributions; the multivariate Gaussian; conditioning via Schur complement; the reparameterization trick that powers VAEs and diffusion.
Understand hypothesis testing, p-values, confidence intervals, and the errors that lurk in every statistical decision.
Where ML loss functions come from. Cross-entropy = MLE for categoricals; MSE = MLE for Gaussian noise; weight decay = Gaussian prior MAP. Fisher information and the natural gradient.
Markov property, transition matrices, stationary distributions, and the Bellman equation — the mathematical foundation of RL, diffusion forward processes, and PageRank.
The algorithm that makes machines learn. Follow a ball rolling downhill through a loss landscape and understand learning rates, momentum, and convergence.
Convex sets and functions, Lagrangian duality, KKT conditions, and the SVM dual derivation — the optimization theory behind RLHF, TRPO/PPO trust regions, and constrained ML.
Measure surprise and information content. Cross-entropy loss, KL divergence, mutual information, Jensen's inequality, and the ELBO that powers VAEs and diffusion.
Brownian motion, Itô's lemma, SDEs, the score function, Langevin dynamics, denoising score matching, and the reverse SDE — the math powering diffusion models.
10 interactive labs — hands-on exercises for this track
Fly over the terrain your optimizer must navigate — peaks are bad, valleys are good
Every neural network is just vectors being multiplied by matrices — build the intuition by dragging arrows on a coordinate plane.
Adjust μ, σ, n, p, and λ and watch the bell curve, bar chart, and shaded probability regions update live.
Warp a 2D plane with any 2×2 matrix and watch the eigenvectors stay fixed in direction — the axes the transformation preserves.
Drag a point along f(x) to watch its tangent line rotate and trace out f'(x) live. Zoom in until the curve BECOMES its tangent.
Trace df/dx backward through f(g(h(x))) — the mechanical pattern that is literally how backprop works.
Drag a slider and watch a straight line morph into a perfect replica of sin, cos, eˣ, ln(1+x), or 1/(1−x).
Click anywhere on a scalar field and watch a particle slide downhill along the negative gradient — always perpendicular to the contours.
Click any point on a 2D function. Gradient, Jacobian, Hessian computed live — eigenvalues classify the curvature as bowl/peak/saddle.
Click surfaces to drop particles. Convex = gradient descent always wins. Non-convex = 10 random inits show how initialization decides your fate.
425 questions across 17 modules — check how well you understood this track.