📄️ Mathematics for AI
Exactly the mathematics you need to understand learning models, explained without needless formalism. 6 hours, applied projects, a 40-question exam and a verifiable certificate.
📄️ 1. Vectors and matrices
Module 1 of the Mathematics for AI premium course: why a vector represents an observation, a matrix a dataset, and how to read dimensions without error — the basic vocabulary of every model.
📄️ 2. Matrix product
Module 2 of the Mathematics for AI premium course: the matrix product as a transformation, the dimension rule, the transpose, and the role of the inverse — the operation at the heart of every model layer.
📄️ 3. Norms, distances, similarity
Module 3 of the Mathematics for AI premium course: measuring the size of a vector (norm), the distance between observations (Euclidean, Manhattan) and the similarity of direction (cosine) — the foundations of search, clustering and embeddings.
📄️ 4. Eigenvalues and PCA
Module 4 of the Mathematics for AI premium course: an intuitive grasp of eigenvalues and eigenvectors, and how principal component analysis (PCA) uses them to compress high-dimensional data without losing the essential.
📄️ 5. Derivatives and gradient
Module 5 of the Mathematics for AI premium course: the derivative as a slope, the gradient as the direction of steepest ascent, and the chain rule that makes backpropagation possible.
📄️ 6. Gradient descent
Module 6 of the Mathematics for AI premium course: the gradient descent algorithm step by step, the decisive role of the learning rate, and the variants (stochastic, mini-batch) that train real models.
📄️ 7. Conditional probability
Module 7 of the Mathematics for AI premium course: probability as the language of uncertainty, independence, conditional probability, and why these notions underpin classification and model evaluation.
📄️ 8. Bayes' theorem
Module 8 of the Mathematics for AI premium course: Bayes' theorem explained through the medical example, the base-rate trap, and the naive Bayes classifier — how to update a belief in light of data.
📄️ 9. Expectation, variance, distributions
Module 9 of the Mathematics for AI premium course: expectation as center, variance and standard deviation as spread, and the common distributions (normal, Bernoulli, uniform) that model real data.
📄️ 10. Bias-variance trade-off
Module 10 of the Mathematics for AI premium course: decomposing a model's error into bias and variance, understanding the optimal balance point, and connecting the trade-off to overfitting and regularization.
📄️ 11. Recap and exam
Final module of the Mathematics for AI premium course: synthesis of the three pillars (linear algebra, calculus, probability), a skills checklist, and the conditions of the 40-question certification exam.