Free quantitative finance & trading curriculum
From mathematical foundations to reproducible trading research. Choose a subject, read its lessons, then use the interactive workspace for practice and labs.
Foundations
Define the mandate. Understand instruments, returns, and capital.
Math & Notation Essentials
Read the symbols, keep track of units, and build a calculation one small step at a time.
8 lessons · notation · units · algebra · modelling
Fund Lab Orientation
A research-to-operations curriculum for building and evaluating a hypothetical investment fund. Start with the mandate and an honest performance record.
1 lessons · your first backtest
Markets, Returns & Capital
Understand what you own, how it earns a return, and where leverage enters the balance sheet.
4 lessons · instruments · compounding · valuation
Trading Different Assets: Instruments, Mechanics & Risk
Understand what you own, how a trade settles, and which quantities belong in your model.
10 lessons · Stocks · ETFs · bonds · futures · commodities · FX · options · crypto · perpetuals · event contracts
Data: Availability, Revisions & Reproducible Research
Reconstruct what a trader could know, then preserve enough evidence to reproduce the decision.
8 lessons · timestamps · vintages · identifiers · survivorship · corporate actions · provenance
Calculus & mathematical models
Study change, accumulation, sensitivities and differential equations from first principles.
Differential Calculus: Limits & Derivatives
Understand change, then learn the rules for measuring it. No finance background is needed.
7 lessons · functions · limits · slopes · chain rule · optimisation
Integral Calculus: Accumulation & Area
Build totals from rates, reverse differentiation, and understand continuous averages.
7 lessons · Riemann sums · antiderivatives · substitution · integration by parts
Multivariable Calculus & Partial Derivatives
Change one input, follow several inputs together, and measure interactions.
5 lessons · partial derivatives · gradients · Hessians · constraints
Differential Equations & Numerical Models
Turn a rate rule into a path, and learn what a numerical solver actually approximates.
4 lessons · ODEs · initial conditions · Euler steps · PDEs
Optimization: Feasibility, Costs & Robust Decisions
Convert forecasts into decisions whose constraints and failure modes can be checked.
8 lessons · feasibility · curvature · duality · robust bounds · transaction costs
Quantitative toolkit
Build the statistical, portfolio, and risk language behind every decision.
Statistics & Probability
Every price move is signal plus randomness. Statistics is how you tell them apart.
9 lessons · entry · validation
Linear Algebra
The moment you hold two positions you are doing linear algebra, whether you know it or not.
4 lessons · portfolio
Time Series Analysis
Markets have memory. Today's price depends on yesterday's, volatility clusters, and trends persist — for a while.
9 lessons · signal · regime
Risk Management
Edge doesn't matter if you size wrong. This is the math that decides whether you are still here next year.
6 lessons · sizing · risk
Stochastic Calculus
From Brownian increments and Itô integration to diffusion models, option prices and hedge sensitivities.
8 lessons · options · hedging
Research & investment
Investigate an edge, develop a strategy, and construct the book.
Research & Backtest Design
Turn a hypothesis into a reproducible experiment, then try to disprove it.
4 lessons · data · inference · validation
Candles, Structures & Pattern Research
Read a chart precisely. Turn a visual observation into a causal rule, then test whether it adds an edge.
13 lessons · OHLCV · structures · indicators · pattern validation
Technical Analysis: Geometry, Structure & Evidence
Turn chart ideas into measurable rules. Separate what a chart shows from what a strategy can earn.
13 lessons · Fibonacci · breakouts · FVG · Heikin-Ashi · Renko · structure
Quant Strategy Development
Find an economic edge, measure the variables that drive it, and build a bot that can express it after costs.
9 lessons · edge discovery · features · trading systems
Portfolio Construction & Factors
Combine forecasts into a book whose risks you can explain and constrain.
4 lessons · allocation · factors · attribution
Rates, Credit & Macro
Connect discount curves, balance sheets, and cross-asset prices.
4 lessons · duration · carry · credit · currencies
FX & Commodities: Quotes, Carry, Curves & Hedges
Trace currency and physical-market cash flows before interpreting a price difference.
8 lessons · bid/ask units · forwards · FX carry · storage · futures margin · rolls · hedges
Arbitrage & prediction markets
Check state payoffs, contract logic, calibration, execution and settlement.
Arbitrage: Payoffs, Financing and Execution
Prove the cash flows and test whether capital survives the path.
8 lessons · state payoffs · parity · carry · baskets · FX · capacity
Prediction Markets: Contracts, Probability and Evidence
Read what settles, score what you forecast, and keep price separate from belief.
8 lessons · binary contracts · resolution · probabilities · scores · calibration
Prediction Strategies: Logic, Sizing and Market Making
Move from a forecast to a defensible, fully accounted decision.
8 lessons · complete sets · logical bounds · sizing · quoting · portfolio risk
Crypto & decentralized finance
Reconcile custody, carry, collateral, pools and on-chain evidence.
Crypto Markets: Instruments, Ownership and Cash Flows
Read the units and claims before measuring returns.
8 lessons · spot · quote currencies · depth · stablecoins · custody · token supply
Crypto Derivatives: Carry, Funding and Liquidation
Reconcile contract units and collateral through the whole price path.
8 lessons · linear · inverse · dated basis · perpetual funding · margin · liquidation
DeFi: AMMs, Liquidity Provision and Lending
Follow reserves, benchmark inventory and test collateral under stress.
8 lessons · constant product · ranges · LP inventory · LVR · lending · liquidation
On-Chain Markets: Data, Oracles and Execution
Separate transactions from economic activity and inclusion from final settlement.
8 lessons · event logs · gas · ordering · oracles · bridges · finality · audit
Options & volatility
Model contingent payoffs, hedging, volatility and implementation limits.
Options: Payoffs, Replication & Hedge Accounting
Understand nonlinear contracts before trusting a pricing or hedging model.
8 lessons · calls · puts · spreads · parity · binomial replication · Greeks · exercise
Volatility: Measurement, Surfaces & Variance Risk
Separate what happened, what is forecast and what an option price implies.
8 lessons · realized variance · EWMA · HAR · implied volatility · term structure · convexity
Systematic strategy development
Build relative-value and HFT systems, validate the search and allocate capital.
Trading Algorithms: A Practical Selection Guide
Choose a method by its job, assumptions and failure modes—not by its popularity.
7 lessons · EWMA · Kalman · ARIMA/GARCH · boosting · allocation · TWAP/VWAP/POV
Statistical Arbitrage: Relative Value to Tradable Portfolios
Define the relationship, estimate the residual, and find out whether convergence survives implementation.
6 lessons · pairs · residuals · cointegration · baskets · structural breaks
High-Frequency Trading: Signals, Queues & Execution
Measure edge at the point where information becomes an order—and an order becomes a fill.
7 lessons · order books · latency · adverse selection · inventory · replay
Strategy Research, Backtesting & Robust Optimisation
Turn an idea into a controlled experiment, and keep parameter search from becoming a search for luck.
6 lessons · point-in-time data · purging · nested tuning · multiple trials · stress tests
Portfolio Theory: Estimation, Risk Budgets & Rebalancing
Allocate across uncertain forecasts, shared risks and implementation constraints.
6 lessons · mean–variance · shrinkage · risk contributions · Bayesian views · turnover
Machine learning & adaptive decisions
Build causal datasets, learn useful forecasts and evaluate sequential policies.
Machine Learning for Quantitative Strategy Development
Choose a useful decision, build an honest dataset, and connect model output to net portfolio value.
8 lessons · labels · regression · classification · trees · calibration · representations
Deep Learning: Sequences, Representations & Financial Decisions
Understand the operations inside the network, then test whether added capacity earns its complexity.
6 lessons · backpropagation · causal CNNs · LSTM · attention · fine-tuning · text
Reinforcement Learning for Trading & Execution
Model decisions through time, design the environment carefully, and test the policy’s assumptions.
8 lessons · MDPs · Bellman equations · Q-learning · policy gradients · offline evaluation
Alternative Data: Measurement, Text & Incremental Value
Turn an unusual dataset into a testable measurement before calling it an edge.
8 lessons · text · event timing · panels · measurement error · incremental forecasts · data costs
Execution & fund operations
Model real-world trading, reconcile results, and defend the fund.
Execution & Market Microstructure
Understand the distance between a forecast price and an executable fill.
4 lessons · orders · slippage · capacity
Fund Operations & Investment Committee
Run the portfolio as an accountable business, from daily NAV to the investment memo.
4 lessons · NAV · fees · liquidity · governance
Put it all together
Connect the tools in a complete, auditable trading research workflow.
Putting It All Together: Build a Complete Trading Research System
Follow one idea from a written hypothesis to a reconciled paper-trading decision.
9 lessons · End-to-end workflow · data contracts · signals · models · portfolio · orders · ledgers · monitoring