The curriculum

Seven tracks, 31 lessons, about 5 hours of reading. Start at Track I if the maths is rusty, or jump to whatever you need. Each lesson ends with a calculator, real strategy specs, or a build command.

IE[X] = Σ x·p(x)

Probability & mathematical foundations

Expected value, Bayes, the distributions markets actually produce, and the linear algebra behind every portfolio.

IIt = μ̂ / (σ̂/√n)

Statistics & time series

Returns, stationarity, regression and the t-stat — the tools for telling signal from noise.

IIISR = (μ − r) / σ

Portfolio construction & risk

Sharpe, mean-variance, Kelly sizing, VaR and drawdowns: how much to bet, and how badly it can go.

IVdS = μS dt + σS dW

Derivatives & volatility

From Brownian motion to Black–Scholes, the Greeks, and why implied volatility smiles.

VdX = θ(μ − X) dt + σ dW

Systematic strategies

Momentum, mean reversion, pairs, carry and grids — what each one is really betting on.

VIP(overfit) ↑ with trials

Backtesting, ML & going live

Honest backtests, overfitting, walk-forward validation, ML labels, and turning research into production.

VIIΔp ≈ σ·√(Q/V)

Market microstructure & execution

Order books, market making, market impact and execution algorithms: where theory meets the tape.