Mathematical Training Built Around Your Goals
QF Academy offers structured mathematical programmes created by mathematicians with industry experience. Through 1-to-1 onboarding, we discuss your goals, background, and target field, then recommend a curriculum built around the training you need.
How QF Works
QF begins with structured programmes designed by mathematicians. During 1-to-1 onboarding, we connect them to your goals, background, constraints, and target field.
Start with onboarding
Your goals, background, available time, and target field are discussed with QF before a curriculum is recommended.
Map the mathematics
We identify the mathematics behind your target area, from linear algebra and analysis to probability, topology, group theory, or functional analysis.
Recommend the curriculum
Your curriculum is built from QF programmes, focus tracks, problem sheets, office hours, assessed work, and project-based specialisations.
Build evidence
You move beyond passive study by completing written work, problem sheets, and projects that can support applications, interviews, research plans, or portfolio building.
Created by mathematicians
QF programmes are designed by human mathematicians, not assembled as generic content playlists.
Connected to technical work
The curriculum connects rigorous mathematics to AI, quantum computing, cryptography, data science, and research-led technical work.
Assessed work
Learners move beyond watching videos by completing problem sheets, written work, and projects.
Foundational Training
QF's foundational programmes cover the mathematical base used across advanced technical work. After onboarding, these modules can be combined into a curriculum covering linear algebra, analysis, probability, topology, group theory, and quantum foundations.
Advanced Linear Algebra for ML
Vector spaces, linear maps, eigenspaces, spectral methods, and the linear algebra used in machine learning.
Measure Theory and Functional Analysis (Module I)
Measure, integration, Hilbert spaces, and functional analysis for probability, quantum mechanics, and advanced analysis.
A Crash Course on ODEs
Ordinary differential equations, phase portraits, stability, and the modelling language used in physics, engineering, and applied mathematics.
Group Theory, Topology & Manifolds
Groups, topological spaces, manifolds, and the geometric language used in modern mathematics, quantum theory, and parts of AI.
Mathematical Foundations for QC
Linear algebra, probability, group theory, tensor products, and Hilbert space methods for quantum computation.
Real Analysis (Module I)
Sequences, limits, continuity, differentiation, and integration, taught with the proof discipline needed for advanced mathematics.
Real Analysis (Module II)
Metric spaces, convergence, compactness, and more advanced analysis, with links to machine learning theory and research.
Focus Tracks
Focus tracks connect foundational mathematics to a technical direction. They are designed for learners who already have a target area and want a guided path through the underlying mathematics.
Algebraic Topology: A Gentle Introduction
Use algebra to study shape. The track covers homotopy, covering spaces, homology, and applications in physics, geometric deep learning, and topological data analysis.
Explore TrackHomotopy and Covering Spaces
Fundamental groups, covering space theory, and applications to topological invariants.
Introduction to Homology Theory
Singular homology, exact sequences, and chain complexes for topological spaces.
Simplicial Homology & Homological Algebra
Computational homology via simplicial complexes and the algebraic machinery behind it.
Modern Applications (AI / Physics)
Geometric deep learning, topological data analysis, and applications in theoretical physics.
Mathematics of Topological Data Analysis (TDA)
Study how topological invariants can be extracted from data through simplicial complexes, homology, persistence, and computation.
Explore TrackGeometric Foundations and Homotopy
Topological spaces, simplicial complexes, and the geometric underpinnings of data analysis.
Homology and Algebraic Machinery
Betti numbers, chain complexes, and the algebraic tools for computing topological features.
Cohomology and Persistence
Persistent homology, barcodes, persistence diagrams, and their stability theorems.
Advanced Topics: Sheaves & Discrete Morse Theory
Sheaf theory, discrete Morse functions, and their applications in data science.
Stochastic Processes (Random Walks): A Rigorous Introduction
A rigorous entry point into stochastic processes through random walks, convergence laws, and measure-theoretic probability.
Explore TrackMeasure-Theoretic Foundations
Sigma-algebras, probability spaces, and the measure-theoretic framework for rigorous probability.
Random Variables & Independence
Measurable functions, independence, expectation, and characteristic functions.
Random Walks & Convergence Laws
Simple random walks, recurrence, transience, and the laws of large numbers.
The Central Limit Theorem & Asymptotics
Weak convergence, CLT proofs via characteristic functions, and asymptotic analysis.
Project-based Specialisations
Advanced mathematical training linked to written work, projects, and stronger evidence of capability.
Lie Groups with Applications
Lie groups, Lie algebras, representation theory, and applications in physics, geometric deep learning, and quantum computing.
Topological Data Analysis
Use simplicial complexes, persistence, and homology to study the shape of data.
Need a Personalised Curriculum?
During 1-to-1 onboarding, QF discusses your background, target field, constraints, and goals. From there, we recommend a curriculum using structured programmes, focus tracks, assessed work, and project-based specialisations.
Career Acceleration Guarantee
Complete an eligible QF specialisation, submit the required work, and apply the training for 8 weeks. If it does not contribute to a job, fellowship, research opportunity, project opportunity, or comparable career outcome, QF will refund the eligible programme fee, subject to the published terms.