Math lessons & courses

Build the mathematical foundation every ML practitioner needs: go from sample spaces and distributions to Bayesian inference and hypothesis testing. By the end you will be able to choose the right distribution for any modelling problem, derive maximum likelihood estimators, reason about uncertainty the Bayesian way, and correctly interpret p-values and confidence intervals.

Master the mathematical backbone of machine learning, signal processing, and scientific computing. By the end you will decompose any matrix into its fundamental subspaces, compute eigenvalues and eigenvectors, apply the SVD for low-rank approximation and compression, and solve least-squares problems — all with geometric intuition and NumPy.

Build the vocabulary that underlies all of ML: sample spaces, discrete and continuous random variables, PMFs, PDFs, and CDFs. Then tour the key distributions — Bernoulli, Binomial, Categorical, Gaussian, Poisson, Exponential, Uniform — with their parameters, mean, variance, and exactly when each appears in practice.

Master the three numbers that summarize any distribution: mean, variance, and standard deviation. Derive linearity of expectation, understand covariance and correlation, then see why the Central Limit Theorem makes the Gaussian unavoidable — with a worked numeric example from scratch.

From raw data to defensible conclusions: derive Maximum Likelihood Estimators for Bernoulli and Gaussian, understand bias-variance in estimation, construct confidence intervals, and learn what p-values actually say — and don't say — including the most common misinterpretation that has corrupted thousands of papers.

Understand what it really means to update beliefs with data. Derive Bayes' theorem from first principles, dissect the roles of prior, likelihood, posterior, and evidence, work through a complete Beta-Binomial conjugate example numerically, and see why the base-rate fallacy trips up even experts.

Vectors are more than arrows — they're the atoms of every ML model, physics engine, and signal processor alive. Build rock-solid intuition for linear combinations, span, independence, basis, and orthogonality, then verify it all in NumPy.

When there's no exact solution, project. When data is high-dimensional, compress. The SVD is the Swiss Army knife that does both — and more. Master orthogonal projection, the normal equations, the Singular Value Decomposition, low-rank approximation, and the pseudoinverse.

A matrix doesn't just hold numbers — it reshapes space. Master the geometric view of matrix-vector multiplication, the four fundamental subspaces, rank, the determinant as a volume-scaling factor, and invertibility — all grounded in NumPy.

Some vectors only get scaled by a matrix — they don't rotate at all. These eigenvectors reveal the skeleton of a linear transformation. Master the eigen-equation, the characteristic polynomial, diagonalization, and why eigenstructure powers PCA, PageRank, and stability analysis.

Every constrained optimization problem has a twin. Learn how to build the Lagrangian, derive the dual problem, and use weak duality, strong duality, and the KKT conditions to certify optima — with worked examples from linear programming and SVMs.