| 1 | Solution of linear systems | Lecture_1.pdf | Linear algebra introduction, closure, systems of linear equations, matrix representation, solution types: no solution, unique solution, infinite solutions, pivot/free variables, matrix operations, inverse, transpose, compact Ax=b form | Very high for Mid-Sem and Comprehensive |
| 2 | Vector spaces, linear independence, basis, rank | Lecture_2.pdf | Groups, Abelian groups, vector spaces, vector subspaces, closure tests, linear combinations, span, linear independence, basis, rank, nullspace/column space ideas | Very high for Mid-Sem and Comprehensive |
| 3 | Analytic geometry | Lecture_3.pdf | Norms, dot product, inner products, bilinear mappings, symmetric positive-definite matrices, lengths, distances, angles, orthogonality, orthonormal basis, Gram-Schmidt ideas | Very high for Mid-Sem and Comprehensive |
| 4 | Matrix Decomposition I | lecture_4.pdf | Determinant, cofactor formula, determinant behaviour under row operations, rank-det relation, eigenvalues/eigenvectors, Cholesky-related positive definite ideas | Very high for Mid-Sem and Comprehensive |
| 5 | Matrix Decomposition II | lecture_5.pdf | Diagonal matrices, diagonalisation, eigendecomposition, spectral theorem for symmetric matrices, SVD, matrix approximation | Very high for Mid-Sem and Comprehensive |
| 6 | Vector Calculus I | lecture_6.pdf | Differentiation of univariate functions, polynomial derivatives, Taylor polynomial/series, partial derivatives, gradients, vector-valued gradients | Very high for Mid-Sem and Comprehensive |
| 7 | Vector Calculus II | lecture_7_edited.pdf | Matrix gradients, useful gradient identities, backpropagation, automatic differentiation, chain rule through neural-network layers | High for Mid-Sem and Comprehensive |
| 8 | Vector Calculus III | lecture_8.pdf | Taylor/Maclaurin series theory, remainder term, two-variable Taylor series, Hessian matrix, maxima/minima, unconstrained optimisation preliminaries | Very high for Mid-Sem and Comprehensive |
| 9 | Continuous Optimisation | Lecture_9.pdf | Gradient descent, negative gradient direction, local minima, step size, line search, convergence intuition, quadratic examples | Very high for Comprehensive; likely useful for quizzes/problems |
| 10 | Nonlinear Optimisation I | Lecture_10.pdf | Initialisation, objective functions in ML, overfitting, feature processing/preprocessing, SGD and practical optimisation behaviour | High for Comprehensive |
| 11 | Nonlinear Optimisation II | Lecture_11.pdf | Difficult topologies: cliffs, valleys, flat regions, curvature; momentum, AdaGrad, RMSProp, Adam | High for Comprehensive |
| 12 | PCA I | Lecture_12.pdf | Dimensionality reduction, PCA problem setting, centred data, covariance, maximum variance perspective, projection perspective | Very high for Comprehensive |
| 13 | PCA II | Lecture_13.pdf | Practical PCA, eigenvector computation, SVD relationship, low-rank approximation, high-dimensional PCA, key PCA steps | Very high for Comprehensive |
| 14 | Mathematical preliminaries for SVM | Lecture 14.pdf | Constrained optimisation, Lagrangian, quadratic programming, primal/dual, weak/strong duality, Slater condition, KKT conditions, kernels, linear classifiers | Very high for Comprehensive |
| 15 | Primal/dual linear SVM | Lecture_15.pdf | SVM primal problem, dual formulation, KKT conditions, support vectors, hinge loss, linear SVM numerical problem, hard/soft-margin direction | Very high for Comprehensive |
| 16 | Nonlinear SVM / kernels | Not clearly uploaded as a separate Lecture 16 PDF | Kernel functions, nonlinear SVM examples; likely partly covered in Lecture 14/15 and webinars | Very high for Comprehensive; gap to fill if Lecture 16 exists |