Foundational Mathematics for Machine Learning
PART I — Mathematical Foundations
Module 1 — Introduction
Class 1
- Machine learning as function approximation and data fitting
- Training, prediction, and model error
- Why geometry, probability, and optimization matter
Module 2 — Linear Algebra for Data
Class 2 – Systems of linear equations and geometric interpretation
Class 3 – Linear mappings and types of mappings (injective, surjective, bijective)
Class 4 – Inverse matrix and Gaussian elimination
Class 5 – Vector subspaces, closure, and linear combinations
Class 6 – Ordered basis, coordinates, and matrix representation
Class 7 – Composition and inverse of linear mappings
Class 8 – Rank, null spaces, and dimensionality
Module 3 — Analytic Geometry of Data
Class 9 – Norms and lengths of vectors
Class 10 – Inner products, angles, and cosine similarity
Class 11 – Orthogonality and Orthonormal Basis (ONB)
Class 12 – Projections onto subspaces
Class 13 – Rotations and geometric transformations
Module 4 — Matrix Decompositions
Class 14 – Determinants and Trace
Class 15 – Eigenvalues and Eigenvectors
Class 16 – Cholesky Decomposition and symmetric positive definite matrices
Class 17 – Singular Value Decomposition (SVD): Theory
Class 18 – SVD for optimal low-rank data representation
Module 5 — Vector Calculus and Optimization
Class 19 – Multivariate functions, partial derivatives, and gradients
Class 20 – Automatic differentiation and computation graphs
Class 21 – Continuous optimization and gradient descent
Class 22 – Constrained optimization: Lagrange Multipliers and Duality
Module 6 — Probability for Data
Class 23 – Foundations of uncertainty and random variables
Class 24 – Probability distributions: Gaussian and Multivariate Gaussian
Class 25 – Mean, variance, and covariance
Class 26 – Sum and product rules; Bayes' Theorem
PART II — Core Machine Learning
Module 7 — When Models Meet Data
Class 27 – Data as vectors; representing real-world information
Class 28 – Empirical Risk Minimization and loss functions
Class 29 – Model selection, generalization, and bias–variance tradeoff
Module 8 — Linear Regression
Class 30 – Linear regression as probabilistic modeling
Class 31 – Least-squares and normal equations
Class 32 – Maximum Likelihood Estimation (MLE) and regularization
Module 9 — Principal Component Analysis
Class 33 – Dimensionality reduction and variance maximization
Class 34 – PCA via Maximum Variance
Class 35 – PCA via Projection
Class 36 – Eigenvector computation and low-rank approximations via SVD
Module 10 — Support Vector Machines
Class 37 – Separating hyperplanes and margin maximization
Class 38 – Soft-margin SVM and slack variables
Class 39 – Dual SVM formulation and Support Vectors
Class 40 – Kernel methods and nonlinear decision boundaries
Module 11 — Projects and Review
Class 41 – Stock Portfolio Optimisation and Eigenfaces
Class 42 – Course Review and Future Directions
Textbook
Deisenroth, M. P., Faisal, A. A., & Ong, C. S. (2020).
Mathematics for Machine Learning. Cambridge University Press.