Self-paced
Advanced Linear Algebra for ML
Vector spaces, linear maps, determinants, matrix decompositions and norms.
View syllabusProgrammes
Browse our foundational curricula, focus tracks and specialisations, or study selected open lecture materials with QF support.
Foundational curricula
Study the mathematical subjects used in further study, from linear algebra and analysis to groups, topology and manifolds.
Included with QFA PASS, QFA PASS PLUS and QFA Research & Career Track.
Self-paced
Measure Theory & Functional Analysis (Module I)
Module I: sigma-algebras, measures, measurable functions and Lebesgue integration; preparation for functional analysis in Module II.
View syllabusSelf-paced
A Crash Course on ODEs
First- and second-order ordinary differential equations, existence and uniqueness, and power-series solutions.
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Group Theory, Topology & Manifolds
Groups and group actions, topological spaces, smooth manifolds and tangent spaces.
View syllabusSelf-paced
Mathematical Foundations for Quantum Computing
Hilbert spaces, tensor products, operators and the mathematics of qubit states and measurements.
View syllabusSelf-paced
Real Analysis (Module I)
Sequences, limits and continuity, with proof-based foundations for real analysis.
View syllabusSelf-paced
Real Analysis (Module II)
Convergence of functions, differentiation, integration, metric spaces and approximation theorems.
View syllabusFocus tracks
Guided study through a defined mathematical subject, with the detailed modules and syllabuses on each track’s page.
Access through QFA PASS PLUS or QFA Research & Career Track, normally one track at a time after preparation checks.
Guided self-paced
Algebraic Topology: A Gentle Introduction
Homotopy, covering spaces, singular and simplicial homology, with selected applications.
Track details and module syllabusesGuided self-paced
Mathematics of Topological Data Analysis (TDA)
Simplicial complexes, homology, persistent homology and the computation of topological features in data.
Track details and module syllabusesGuided self-paced
Stochastic Processes (Random Walks): A Rigorous Introduction
Measure-theoretic probability, random walks, convergence laws and the central limit theorem.
Track details and module syllabusesSpecialisations
Connect advanced mathematics with applications and project work.
Access through QFA PASS PLUS or QFA Research & Career Track, subject to preparation checks.
Project-based
Lie Groups with Applications
Lie groups, Lie algebras and representation theory, with applications in physics, machine learning and quantum computing.
View syllabusProject-based
Topological Data Analysis with Applications
Simplicial complexes, homology and persistence, with computational methods for analysing the shape of data.
View syllabusSupported study
Study selected external lecture materials with QF’s own study and assessment support.
QF support is included with QFA PASS, QFA PASS PLUS and QFA Research & Career Track.
Open lectures + QF assessment
Matrix Methods in Data Analysis, Signal Processing, and Machine Learning
Linear algebra and matrix methods for data analysis, signal processing and machine learning.
Open lectures + QF assessment
Matrix Calculus for Machine Learning and Beyond
Matrix differentiation and differential calculus for machine learning.
Open lectures + QF assessment
Applied Category Theory
Categories, functors and compositional methods for systems, networks and applied modelling.
Preparing for an advanced programme
If you need more preparation before starting a focus track or specialisation, we’ll help you identify what to study using our foundational curricula and curated external resources.
Book a free 45-minute discovery callMembership and support
Your membership plan determines programme access and the teaching, feedback and mentoring available to you.