The map

How to Become a Quant

The whole field, in dependency order. Each stage builds on the ones above it. Green nodes are published lessons, click any to start; the rest are being written. This is the spine of the platform: the concepts feed the strategies, and the same material shows up in interviews.

Foundational Core Advanced In progress

1
Mathematical FoundationsFoundational
Probability, linear algebra, and optimization, the language everything else is written in.
Probability Spaces Random Variables & Distributions Expectation, Variance & Moments Common Distributions Moment Generating Functions The Law of Large Numbers The Central Limit Theorem Bayes' Theorem Markov Chains Martingales Linear Algebra for Quants Eigenvalues & Eigenvectors Singular Value Decomposition Positive Semidefinite Matrices Convex Optimization Lagrange Multipliers & KKT Conditions
2
Statistics & EconometricsCore
Estimation, inference, regression, and time series, done rigorously, with the failure modes.
Bias, Variance, and the Quality of Estimators Maximum Likelihood Estimation (MLE)Method of Moments and GMM Hypothesis Testing Confidence Intervals p-values and Multiple Testing Ordinary Least Squares (OLS)The Gauss–Markov Theorem Heteroskedasticity Autocorrelation and Serial Correlation Multicollinearity Endogeneity and Instrumental Variables Stationarity ARMA Models GARCH Volatility Models Unit Roots and the ADF Test Cointegration Ridge and LASSO Regularization Bootstrap and Resampling Bayesian Inference
3
Portfolio Construction & RiskCore
From Markowitz to risk parity, covariance estimation, Kelly sizing, and tail risk.
Alpha (α)Beta (β)Volatility MPT (Harry Markowitz)The Efficient Frontier The Capital Asset Pricing Model (CAPM)Pitfalls of Mean-Variance Optimization Covariance Matrix Estimation Shrinkage Ledoit-Wolf Covariance Shrinkage The Black-Litterman Model Risk Parity Hierarchical Risk Parity (López de Prado)Factor Risk Models The Kelly Criterion Position Sizing Vol Targeting Sharpe Ratio Sortino Ratio Information Ratio Calmar Ratio Max Drawdown Value at Risk (VaR)Expected Shortfall (CVaR)Coherent Risk Measures Portfolio Capacity
4
Derivatives & VolatilityAdvanced
Stochastic calculus, Black-Scholes, the Greeks, and the volatility surface.
Brownian Motion Itô's Lemma Risk-Neutral Pricing The Black-Scholes Model Put-Call Parity The Option Greeks Delta-Hedging P&L Implied Volatility The Volatility Smile and Skew Local Volatility and Dupire's Formula Stochastic Volatility and the Heston Model The SABR Model Variance Swaps The VIX Index The Term Structure of Volatility Girsanov's Theorem The Feynman-Kac Theorem Exotic Options
5
Systematic Strategies & AlphaAdvanced
Market efficiency, the factor zoo, signal construction, and stat-arb.
Market Efficiency (The EMH)Factor Investing The Fama-French Factor Models Momentum The Value Factor Carry The Low-Volatility Anomaly The Quality Factor Signal Construction Alpha Decay Cross-Sectional vs. Time-Series Strategies Mean Reversion Pairs Trading Statistical Arbitrage Trend Following Regime Detection
6
Backtesting & ML in FinanceAdvanced
How backtests lie, and the validation discipline that separates signal from noise.
Backtest Design Look-Ahead Bias Survivorship Bias Data-Snooping Bias Overfitting Walk-Forward Analysis Cross-Validation for Time Series Purged & Embargoed Cross-Validation The Deflated Sharpe Ratio Feature Engineering for Finance Triple-Barrier Labeling Tree Ensembles in Finance Backtest Overfitting Transaction Costs
7
Market Microstructure & ExecutionAdvanced
Order books, adverse selection, market impact, and optimal execution.
Order Book Mechanics Market vs. Limit Orders Bid-Ask Spread Decomposition Adverse Selection The Glosten-Milgrom Model The Kyle Model Market Impact The Square-Root Impact Law The Almgren-Chriss Model Optimal Execution TWAP, VWAP & POV The Avellaneda-Stoikov Model Latency & High-Frequency Trading Transaction Costs

→ Interview Prep

Turn this knowledge into offers: 300 questions, mocks, company guides.

→ Strategy Database

See the concepts assembled into full systematic strategies.

→ Learning Tracks

Work through each stage with progress tracking.