Foundational curriculum
Advanced Linear Algebra for ML
Study vector spaces, linear maps, matrix decompositions and norms, with applications to machine learning.
Read the syllabus PDFMathematical training
for your technical goals
University-level mathematics programmes in abstract algebra, analysis, geometry and topology for applied researchers, engineers and students working in AI, quantum computing, cryptography and other emerging technologies.
What our members say
Read the impact report
I'm especially grateful to Brian Hepler, PhD, for his exceptional teaching and to the QF Academy team, particularly Bamborde Balde, for providing such a high-quality learning experience. It's not often you find a course combining advanced theory with real-world quantum applications so effectively.
Claudia Zendejas-Morales
Physicist
I gained valuable insights from completing a Quantum Formalism course on Group Theory, Topology and Manifolds - useful for my PhD in QML. My mentor Bamborde Balde met with me personally to tailor my study plan and made invaluable comments.
Daniel Goldsmith
Senior Quantum Technologist & PhD Researcher in QML
Thank you to Quantum Formalism for making abstract mathematics more accessible to industry-based researchers. It's been a rewarding experience exploring the different phases.
Senaka Samarasekera
AI ML Algorithms and Signal Processing Engineer
This course significantly improved my understanding of proof-based linear algebra, provided valuable feedback from PhD mathematicians, and enhanced my communication skills in a technical context.
Hanseul Kim
Deep Learning Researcher
My first foray into proper metric topology while proving everything as we went. Everyone was very welcoming and enthusiastic. The end result was an incredibly rewarding experience.
Dave Jones
VP, Lead Software Engineer
I’m following Group Theory 360 and very much appreciate the Lie Theory and Cryptography-related examples.
I studied this material years ago, and it is wonderful to have the chance to refresh and update my knowledge and to see recent applications.
Eddie (Edward) Jennings
Chief Engineer, Scientist
Commercial Solutions for Classified
Solution Architect, Technical Fellow
Explore our programmes
Explore foundational curricula and specialisations.
Foundational curriculum
Group Theory, Topology & Manifolds
Study groups, group actions, topological spaces and smooth manifolds, with examples from Lie groups.
Read the syllabus PDFFoundational curriculum
Measure Theory & Functional Analysis
Module I: Sigma-algebras, measures, measurable functions, Lebesgue integration and convergence theorems.
Read the Module I syllabus PDFSpecialisation
Topological Data Analysis with Applications
Use simplicial complexes, persistence and homology to study the shape of data.
Read the syllabus PDFSpecialisation
Lie Groups with Applications
Study Lie groups, Lie algebras and representation theory, with applications in physics, geometric deep learning and quantum computing.
Read the syllabus PDFHow studying works
Study lectures and notes, complete problem sheets and written submissions, and attend the sessions included in your plan.
Choose a programme and plan
Review the programme syllabus and plan entitlements. You can book a free discovery call before enrolling if you have questions about your preparation.
Complete onboarding and get access
After joining, schedule a 1-to-1 onboarding call to discuss your background and available study time. QF recommends a study sequence and provides login details for your materials.
Study and submit work
Work through lectures and problem sheets, write mathematical arguments and submit assignments. Live sessions, office hours, feedback and mentoring depend on your plan.
Applications
These fields draw on algebra, analysis, geometry, topology and probability.
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Artificial intelligence
Geometric deep learning, probabilistic modelling and optimisation.
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Quantum computing
Quantum algorithms, quantum error correction and quantum machine learning.
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Cryptography
Post-quantum cryptography, homomorphic encryption and zero-knowledge proofs.
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Condensed matter physics
Topological phases, quantum magnetism and strongly correlated systems.
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Bioinformatics
Sequence analysis, gene regulatory networks and phylogenetic inference.
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Computer science
Formal verification, programming language semantics and algorithm analysis.
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Computational chemistry
Molecular dynamics, electronic structure and reaction kinetics.
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Computational physics
Fluid dynamics, wave propagation and inverse problems.
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Financial modelling
Derivative pricing, portfolio optimisation and risk modelling.
Plans and pricing
Plans differ in programme access, live teaching, feedback and mentoring. Every plan includes 1-to-1 onboarding.
Monthly billing · Prices in US dollars (USD)
QFA PASS
$79.99 / month
For independent members studying foundational materials and using group office hours.
- Foundational programmes and problem sheets
- Selected live bootcamps and workshops
- Biweekly group office hours
QFA PASS PLUS
$179.99 / month
For members adding focus tracks, specialisations and monthly individual office hours.
- Everything in QFA PASS, plus focus tracks and specialisations
- Monthly 1-to-1 office hours
- Career direction support
QFA Research & Career Track
$479.99 / month
For members seeking individual assignment feedback, research or career mentoring and project review.
- Everything in QFA PASS PLUS, with feedback on individual assignments
- Regular 1-to-1 office hours
- Research or career mentoring and portfolio review
Custom training
Mathematical training for companies, universities and research groups, tailored to your team’s background and requirements.
Frequently asked questions
What mathematical background do I need?
The background you need depends on the programme. We’ll discuss what you’ve already studied and help you choose a suitable starting point. If you need more preparation before beginning a focus track or specialisation, we’ll help you work through the relevant material using our foundational curricula and curated external resources.
Can I study alongside work or university?
You can work through the self-paced material around your other commitments. For programmes with scheduled sessions or submission deadlines, we’ll discuss the timetable and expected workload so you can decide what you can realistically take on.
Are programmes self-paced or live?
Our foundational curricula are self-paced, and we also offer live bootcamps, guided focus tracks and project-based specialisations. The programme page explains the format, while your membership plan determines access to live teaching, office hours and other support.
What feedback and office hours are included?
QFA PASS includes fortnightly group office hours, while QFA PASS PLUS adds a monthly one-to-one session. The QFA Research & Career Track includes regular one-to-one sessions, feedback on individual assignments, and research or career mentoring. See the plans and pricing page for the full comparison.
What happens after I join?
We’ll arrange a one-to-one onboarding call to discuss your interests, mathematical background and available study time. Together, we’ll agree on where to begin and what to study next. You’ll also receive login details for the programme materials included in your membership.
Can I speak to someone before joining?
Yes. You can book a free 45-minute discovery call to ask questions and discuss which programmes might suit you. You don’t need to have chosen a programme beforehand. This call is optional and separate from the onboarding included after you join.
Join QF Academy
Choose a plan to enrol, or book a free discovery call to discuss your preparation and available study time.