Mathematical Prerequisites¶
This appendix is a self-contained reference for the mathematics, probability, and statistics that the course builds on. It is not a detour — quantitative trading is applied probability and statistics, and Part III — Statistics for Trading links directly into these pages wherever a lesson leans on a formal result.
How to use this appendix¶
- If you have a quantitative background, skim the part titles and move on. Come back when a course lesson cites a specific result.
- If you are newer to probability, work through Parts I–VIII in order — they build from counting principles up to the Central Limit Theorem and Markov processes, which is exactly the toolkit regime models and Monte Carlo methods assume later.
- The statistics parts (X–XVII) cover estimation, hypothesis testing, regression, model selection, multiple testing, and Bayesian methods — the machinery behind every "is this strategy actually profitable?" question the course asks.
- Part XVIII connects the formal results back to trading: sizing, risk, microstructure, and regime detection.
Contents¶
| Part | Focus |
|---|---|
| Part I — Mathematical Foundations | Sets, counting, notation, series, and linear algebra |
| Part II — Foundations of Probability | Sample spaces, axioms, conditioning, Bayes' rule, and independence |
| Part III — Random Variables | CDFs, PMFs, PDFs, joint and conditional distributions, transformations |
| Part IV — Expectation and Moments | Expectation, variance, covariance, correlation, and the total laws |
| Part V — Common Probability Distributions | The standard discrete and continuous families |
| Part VI — Multivariate Probability | Random vectors, covariance matrices, and the multivariate Gaussian |
| Part VII — Asymptotic Theory | Laws of large numbers, the CLT, and the mapping theorems |
| Part VIII — Stochastic Processes | Arrival processes, Markov chains, HMMs, and Brownian motion |
| Part IX — Monte Carlo Methods | Simulation, sampling, variance reduction, and resampling |
| Part X — Foundations of Statistics | Samples, sampling distributions, and statistical models |
| Part XI — Parameter Estimation | Point and interval estimation, ML, moments, and Bayesian estimates |
| Part XII — Hypothesis Testing | Tests, p-values, errors, power, and the main test families |
| Part XIII — Regression and Statistical Models | Linear and generalized linear models, regularization, diagnostics |
| Part XIV — Model Selection | Bias–variance, cross-validation, information criteria |
| Part XV — Multiple Testing | Corrections for many comparisons and data snooping |
| Part XVI — Bayesian Statistics | Priors, posteriors, conjugacy, updating, and prediction |
| Part XVII — Statistical Computing | Optimization, EM, and MCMC |
| Part XVIII — Applications to Quantitative Finance | Sizing, risk, microstructure, and regime detection |
Note
Much of this material was migrated from an earlier site and is kept mathematically rigorous, with proofs in collapsible blocks and R-based Monte Carlo simulations. Pages marked Draft are placeholders for planned content.