MFML Lecture to Course Content Map

Mon, 01 Jan 0001 00:00:00 +0000

MFML Lecture to Course Content Map #

This file maps the uploaded Maths lecture PDFs and webinar PDFs against the official course handout/contact-session plan. It is intended as an exam preparation index and as a source map for future Hugo Markdown notes.

Course identity #

Course: Mathematical Foundations for Machine Learning
Course code: AIML ZC416
Main areas: linear algebra, vector spaces, matrix decompositions, vector calculus, optimisation, PCA, and SVM.

Official module structure #

Module	Course handout area	Main ideas	Uploaded lecture coverage
M1	Solution of linear systems	Systems of equations, matrices, solving Ax = b	Lecture 1, Webinar 1
M2	Vector spaces and analytic geometry	Vector spaces, linear independence, basis, rank, norms, inner products, angles, orthogonality, orthonormal basis	Lecture 2, Lecture 3, Webinar 1
M3	Matrix decomposition methods	Determinant, trace, eigenvalues, eigenvectors, Cholesky, eigendecomposition, diagonalisation, SVD, matrix approximation	Lecture 4, Lecture 5, Webinar 1, Webinar 2
M4	Vector calculus	Univariate differentiation, partial derivatives, gradients, matrix gradients, Taylor/Maclaurin series, Hessian, backpropagation, automatic differentiation	Lecture 6, Lecture 7, Lecture 8, Webinar 2
M5	Continuous optimisation	Gradient descent, constrained optimisation, Lagrange multipliers, convex optimisation	Lecture 9, Lecture 14, Webinar 2, Webinar 3, Webinar 4
M6	Nonlinear optimisation	Learning rate, initialisation, SGD, feature preprocessing, local optima, cliffs/valleys, momentum, AdaGrad, RMSProp, Adam	Lecture 10, Lecture 11, Webinar 3
M7	Dimensionality reduction, PCA, SVM	PCA perspectives, low-rank approximation, high-dimensional PCA, practical PCA, SVM preliminaries, primal/dual SVM, kernels	Lecture 12, Lecture 13, Lecture 14, Lecture 15, Webinar 4

Contact session by lecture #

Session	Course handout topic	Uploaded file	What the lecture appears to cover	Exam relevance
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

Webinar mapping #

Webinar file	Main role	Best linked lectures	Exam use
`Webinar_1.pdf`	Problem sheet on linear systems, REF/RREF, column space, nullspace, row independence, subspaces, inner products, Cauchy-Schwarz, Cholesky, eigenvalues	Lectures 1-5	Excellent for Mid-Sem problem practice
`Webinar_2.pdf`	Worked problems on maxima/minima, eigenvalues/spectral decomposition, gradient-related calculations and PCA-style examples	Lectures 4-9, 12-13	Excellent for Mid-Sem revision and Comprehensive practice
`Webinar_3.pdf`	Gradient descent algorithm, step-size derivation for quadratic functions, worked gradient descent examples	Lectures 8-11	Excellent for optimisation exam problems
`webinar_4.pdf`	Appears linked to optimisation/SVM/PCA practice based on uploaded set; use as problem-solving supplement after Lecture 12 onwards	Lectures 12-15	Comprehensive exam practice

Mid-Sem focus #

The course handout states that the Mid-Semester Test covers Weeks 1-8. So for Mid-Sem, focus on:

DNN Formula and Numerical Sheet

Mon, 01 Jan 0001 00:00:00 +0000

DNN Formula and Numerical Sheet #

This page consolidates the most useful Deep Neural Networks formulas and numerical patterns for revision.

It is designed for preparation and should be used together with the topic pages.

Revision strategy:
Do not only memorise formulas.

For each formula, know:

what each symbol means

when to apply it

how to substitute values carefully

what the output shape or answer represents

1. Artificial Neuron #

Weighted Sum ☆ #

\[ z = \sum_{i=1}^{n} w_i x_i + b \]

Vector form:

Exam on Arshad Siddiqui