MatheLinuxQuant learning system
MatheLinux
Start with competing exponential clocks — dense notes, then move a lab control. That is the MatheLinux loop.
One sitting: lesson + interactive lab. Stochastic undergrad, calculus, ML, QML, stats, and linear algebra are in the catalog.
Stochastic calculus
Black–Scholes and Itô's lemma
dSₜ = μSₜdt + σSₜdWₜ
Wₜ ∼ BM(Σₜ)dƒ(Sₜ,t) = (∂ₜƒ + μSₜ∂ₛƒ + ½σ²Sₜ²∂ₛₛƒ)dt + σSₜ∂ₛƒdWₜDerive the pricing PDE→Recommended sequence
Intermediate
Why Brownian motion underprices tail risk, and how Lévy processes fix it.
Open courseIntermediate
Self-exciting events, volatility clustering, and order-book dynamics.
Open courseIntermediate
The Heston model and the Girsanov change of measure behind modern pricing.
Open courseBeginner → Intermediate
The math a working quant actually uses — probability, differential equations, stochastic calculus, the Black–Scholes model, and numerical methods — built from the ground up with full derivations, worked examples, and graded problems.
Open courseBeginner → Intermediate
The other half of quant math — vectors, matrices, eigenvalues, SVD, PCA, least-squares regression, and convex optimization — built to where you can extract PCA factors and solve a Markowitz portfolio by hand.
Open courseFoundational
The calculus a quant uses every day — limits, derivatives, Taylor series, integration, multivariable gradients and Lagrange multipliers, and vector calculus — built with full derivations and worked examples.
Open courseAdvanced
The rigorous foundation under calculus and probability — completeness, sequences and series, topology and continuity, Riemann and Lebesgue integration, and an introduction to functional analysis (Banach/Hilbert/L^p).
Open courseAdvanced
Probability made rigorous — sigma-algebras and measures, random variables as measurable maps, expectation as a Lebesgue integral, conditional expectation as an L^2 projection, and the limit theorems (LLN, CLT, extreme value) that underpin risk.
Open courseAdvanced
The frontier of derivatives valuation — backward SDEs and nonlinear Feynman–Kac, counterparty credit risk, the full XVA stack (CVA/DVA/FVA/KVA), and the Monte-Carlo and deep-BSDE methods that price them.
Open courseIntermediate → Advanced
The implementation half of quant work — modern C++, numerically-sound pricers, and the high-performance computing (cache, SIMD, threads, GPU) that production pricing engines run on.
Open courseFeatured course / Intermediate
Reviews to simulation to DTMC/MRP/DP/MDP, with an interactive lab closing every chapter.
Curriculum map
Every stage names its mathematical dependency and its production destination.
Open the full prerequisite tree →The equation, implementation, experiment, and review remain connected—so a shortcut never loses its assumptions.
State the dynamics, measure, boundary conditions, and every modeling assumption.
∂V/∂t + ½vS²Vₛₛ + ρξvSVₛᵥ + ½ξ²vVᵥᵥRead the model →Translate the operator into a stable scheme and make numerical error observable.
step_x(i, j, &p, dt); // ADI sweepStudy the implementation →Compare the model with market behavior, then stress parameters and assumptions.
model − market · p95 error · stabilityRun the reasoning →Keep results, feedback, and the next prerequisite attached to the work.
model → test → evidence → feedbackSee what follows →The math a working quant actually uses — probability, differential equations, stochastic calculus, the Black–Scholes model, and numerical methods — built from the ground up with full derivations, worked examples, and graded problems.
Start the foundation →Probability
Stochastic processes
Stochastic calculus
PDE & numerics
Keep the curriculum open for free. Subscribe when you need deeper lessons, practice, submissions, and feedback.
One membership. The whole path.
Free covers the map and first lessons. Pro adds the rest.
Pro price
$29/mo
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Use this to start on the map.
Use Pro when you are ready for the full path, submissions, and interviews.
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