MatheLinuxQuant learning system
Math, pricing, risk, and systems.
Quant curriculum tree
Start at the root, then pick a direction. Modules in the same row can be studied in parallel; the detail panel shows real prerequisites (a graph, not one forced queue).
Select module →updates the detail panel; underlined course actions navigate to a course.
Direction
Probability, stochastic models, pricing, and frontier research. Same-row modules can run in parallel.
Graph path · same row = parallel
Direction
Linear algebra, numerics, stochastic calculus, and portfolio decisions — not a single queue.
Graph path · same row = parallel
Direction
Calc/LA/ODEs/numerics feed systems and market-data work. ML is a side branch, not a forced last step.
Graph path · same row = parallel
Algebra, probability, and proof basics.
M1
Algebra, linear systems, and intro probability.
Module 1
Algebra, linear systems, and intro probability.
1.1 Pre-Calculus & Mathematical Logic
1.2 Introductory Linear Algebra
1.3 Introductory Probability & Statistics
Reference texts
Strang — Introduction to Linear Algebra · DeGroot & Schervish — Probability and Statistics
Calculus and real analysis.
M2
Derivatives, integrals, gradients, and multivariable calculus.
Module 2
Derivatives, integrals, gradients, and multivariable calculus.
2.1 Single-Variable Calculus
2.2 Multivariable Calculus
2.3 Vector Calculus
Reference texts
Stewart — Multivariable Calculus · Apostol — Calculus Vol. 2
M3
Sequences, limits, measure, and integration.
Module 3
Sequences, limits, measure, and integration.
3.1 Reals, Sequences & Series
3.2 Topology & Continuity
3.3 Riemann & Lebesgue Integration
3.4 Metric & Functional Analysis
Reference texts
Rudin — Principles of Mathematical Analysis · Kreyszig — Introductory Functional Analysis
Linear algebra and probability.
M4
Matrix factorizations, eigenvalues, and optimization geometry.
Module 4
Matrix factorizations, eigenvalues, and optimization geometry.
4.1 Matrix Decompositions
4.2 Spectral Theory
4.3 Quadratic Forms & Optimization Geometry
4.4 Applied Linear Algebra in Finance
Reference texts
Horn & Johnson — Matrix Analysis · Trefethen & Bau — Numerical Linear Algebra
M5
Measures, expectation, conditioning, and limit theorems.
Module 5
Measures, expectation, conditioning, and limit theorems.
5.1 Measure Theory Foundations
5.2 Integration & Expectation
5.3 Conditional Expectation
5.4 Limit Theorems
5.5 Multivariate & Extreme Value
Reference texts
Durrett — Probability: Theory and Examples · McNeil, Frey & Embrechts — Quantitative Risk Management
ODEs, PDEs, and numerics.
M6
ODEs, PDEs, and the Black–Scholes PDE.
Module 6
ODEs, PDEs, and the Black–Scholes PDE.
6.1 Ordinary Differential Equations
6.2 Partial Differential Equations
Reference texts
Evans — Partial Differential Equations · Wilmott, Howison & Dewynne — Mathematics of Financial Derivatives
M7
Root finding, quadrature, Monte Carlo, and finite differences.
Module 7
Root finding, quadrature, Monte Carlo, and finite differences.
7.1 Numerical Linear Algebra
7.2 Root Finding & Optimization
7.3 Interpolation & Quadrature
7.4 Numerical ODEs & PDEs
Reference texts
Glasserman — Monte Carlo Methods in Financial Engineering · Duffy — Finite Difference Methods in Financial Engineering
Itô calculus and SDEs.
M8
Brownian motion, Itô calculus, SDEs, and jumps.
Module 8
Brownian motion, Itô calculus, SDEs, and jumps.
8.1 Discrete-Time Processes
8.2 Brownian Motion
8.3 Itô Calculus
8.4 Jumps & Lévy Processes
Reference texts
Shreve — Stochastic Calculus for Finance II · Øksendal — Stochastic Differential Equations
Pricing, Greeks, vol, and rates.
M9
No-arbitrage pricing, Greeks, exotics, rates, and vol.
Module 9
No-arbitrage pricing, Greeks, exotics, rates, and vol.
9.1 No-Arbitrage Pricing
9.2 Black–Scholes & the Greeks
9.3 Exotic & American Options
9.4 Rates & Volatility Models
9.5 Risk & Portfolio
Reference texts
Hull — Options, Futures, and Other Derivatives · Gatheral — The Volatility Surface · Brigo & Mercurio — Interest Rate Models
Control, rough vol, credit, and ML.
M10
Control, rough vol, BSDEs, credit, and convex optimization.
Module 10
Control, rough vol, BSDEs, credit, and convex optimization.
10.1 Optimal Control & Malliavin
10.2 Rough Volatility & ML
10.3 BSDEs, XVA & Credit Risk
10.4 Convex Optimization
Reference texts
Boyd & Vandenberghe — Convex Optimization · Nualart — The Malliavin Calculus · Crépey — Counterparty Risk and Funding
Build the production layer.
M11
Load balancing, Redis, queues, observability, and reliability.
Module 11
Load balancing, Redis, queues, observability, and reliability.
11.1 Internet-Facing Architecture
11.2 Redis, Caching & State
11.3 CDN & Edge Delivery
11.4 Asynchronous Systems
11.5 Reliability & Operations
Reference texts
Kleppmann — Designing Data-Intensive Applications · Burns — Designing Distributed Systems
M12
Market data, risk checks, order routing, and replay.
Module 12
Market data, risk checks, order routing, and replay.
12.1 Data Ingestion & Normalization
12.2 Strategy and Risk Services
12.3 Execution & Order Routing
12.4 Backtest to Live
12.5 Performance Engineering
Reference texts
Aldridge — High-Frequency Trading · Kissell — The Science of Algorithmic Trading and Portfolio Management
Regression through deep learning, applied to finance.
M13
Regression, classification, trees, deep learning, and the statistical traps that break backtests.
Module 13
Regression, classification, trees, deep learning, and the statistical traps that break backtests.
13.1 The Learning Map
13.2 Regression & Classification
13.3 Resampling & Model Selection
13.4 Flexible & Ensemble Methods
13.5 Deep Learning & Modern AI
13.6 Unsupervised & Statistical Rigor
Reference texts
James, Witten, Hastie, Tibshirani & Taylor — An Introduction to Statistical Learning
Start with the foundations
Start with probability and linear algebra.
13 modules mapped from math to systems.
