Course Catalog - Academic Year 2026

Start Building Your
Mathematical Advantage

An outcomes-driven curriculum designed to bridge the gap between abstract mathematics and practical applications across multiple domains. Think of QF Academy as an exclusive training environment for serious professionals building mathematical fitness at a high level.

Foundational Core Courses

Master the essential mathematics for an advanced career in science and technology. Available on-demand, at your pace.

Advanced Linear Algebra
FC - 01
Foundational

Advanced Linear Algebra for ML

Bridge the gap between engineering and research with a rigorous treatment of vector spaces and linear maps.

Measure Theory
FC - 02
Foundational

Measure Theory and Functional Analysis (Module I)

Explore measure, integration, and Hilbert spaces - essential for modern probability theory and quantum mechanics.

ODEs
FC - 03
Foundational

A Crash Course on ODEs

Model and solve differential equations describing dynamical systems in physics, engineering, and finance.

Group Theory
FC - 04
Foundational

Group Theory, Topology & Manifolds

Explore essential mathematical structures for advanced applications in AI, ML, and Quantum Computing.

Quantum Computing Maths
FC - 05
Foundational

Mathematical Foundations for QC

Build a rigorous mathematical foundation in linear algebra, probability, and group theory for quantum computing.

Real Analysis I
FC - 06
Foundational

Real Analysis (Module I)

Build the rigorous foundation essential for understanding machine learning theory and advanced algorithms.

Real Analysis II
FC - 07
Foundational

Real Analysis (Module II)

Continue into advanced analysis, covering topics essential for deep learning theory and modern research.

Focus Tracks

Intensive, module-based courses aimed at fast-tracking you into specific advanced mathematical territories for frontier research in AI, Quantum, and other emerging fields. Tracks rotate periodically to cover emerging research areas.

Focus Track 0126

Algebraic Topology: A Gentle Introduction

Unlock the deep connections between algebra and geometry. A critical toolkit for theoretical physics, geometric deep learning, and topological data analysis.

Get Started
Module I
Homotopy and Covering Spaces

Fundamental groups, covering space theory, and applications to topological invariants.

Syllabus
Module II
Introduction to Homology Theory

Singular homology, exact sequences, and chain complexes for topological spaces.

Syllabus
Module III
Simplicial Homology & Homological Algebra

Computational homology via simplicial complexes and the algebraic machinery behind it.

Syllabus
Module IV
Modern Applications (AI / Physics)

Geometric deep learning, topological data analysis, and applications in theoretical physics.

Syllabus
Focus Track 0226

Mathematics of Topological Data Analysis (TDA)

Explore the intersection of algebraic topology and computer science, focusing on algorithms to compute topological invariants from discrete data.

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Module I
Geometric Foundations and Homotopy

Topological spaces, simplicial complexes, and the geometric underpinnings of data analysis.

Syllabus
Module II
Homology and Algebraic Machinery

Betti numbers, chain complexes, and the algebraic tools for computing topological features.

Syllabus
Module III
Cohomology and Persistence

Persistent homology, barcodes, persistence diagrams, and their stability theorems.

Syllabus
Module IV
Advanced Topics: Sheaves & Discrete Morse Theory

Sheaf theory, discrete Morse functions, and their applications in data science.

Syllabus
Focus Track 0326

Stochastic Processes (Random Walks): A Rigorous Introduction

A comprehensive entry point into stochastic processes, focusing on the mathematical theory of Random Walks. Moves beyond intuition to establish firm foundations in Measure Theory and rigorous analysis.

Get Started
Module I
Measure-Theoretic Foundations

Sigma-algebras, probability spaces, and the measure-theoretic framework for rigorous probability.

Syllabus
Module II
Random Variables & Independence

Measurable functions, independence, expectation, and characteristic functions.

Syllabus
Module III
Random Walks & Convergence Laws

Simple random walks, recurrence, transience, and the laws of large numbers.

Syllabus
Module IV
The Central Limit Theorem & Asymptotics

Weak convergence, CLT proofs via characteristic functions, and asymptotic analysis.

Syllabus

Project-based Specialisations

Apply your knowledge to become a subject matter expert. Complete a specialisation to qualify for our outcomes-driven success guarantee.

Lie Groups
SP - 01
Specialisation

Lie Groups with Applications

An advanced course on Lie groups and their applications in physics, geometric deep learning, and quantum computing.

TDA
SP - 02
Specialisation

Topological Data Analysis

Discover how to analyse the shape and structure of complex datasets using topological methods for novel insights in data science.

Outcomes-Driven Guarantee

Complete a specialisation, apply your skills for 8 weeks. If you don't land a job, fellowship, or meaningful new opportunity - we give you a full refund. No questions asked.