Mathematics & Statistics
Phase 2 of the quantitative learning path. These articles build the mathematical and statistical foundation you need before moving to ML foundations (Phase 3) and ML × Quant (Phase 4).
16 articles ~1.1 h
Probability
- What Is Probability? Sample spaces, events, probability axioms, conditional probability, independence
- Random Variables and Probability Distributions Discrete and continuous random variables, PMF, PDF, CDF, expectation, variance
- Common Probability Distributions Normal, lognormal, binomial, Poisson, exponential, t-distribution
- Bayes' Theorem and Conditional Probability Bayes' theorem, prior vs posterior, Bayesian updating
- Law of Large Numbers and Central Limit Theorem LLN, CLT, and why they justify modeling assumptions
Statistics
- Descriptive Statistics: Mean, Median, Mode Mean, median, variance, standard deviation, skewness, kurtosis
- Hypothesis Testing: P-Values and Significance H₀/H₁, p-values, t-tests, Type I/II errors, significance levels
- Confidence Intervals Point estimates, interval estimates, 95% CI interpretation, CI vs credible interval
- Regression Analysis Basics Simple linear regression, least squares, R², multiple regression introduction
- Time Series: Stationarity and Autocorrelation Stationarity, ACF, correlograms, Ljung-Box test, first-differencing
Linear Algebra
- Vectors and Matrices Vector and matrix definitions, operations, dot product, transpose, geometric interpretation
- Matrix Operations Matrix multiplication, identity, inverse, determinant, properties
- Eigenvalues and Eigenvectors Eigendecomposition, symmetric matrices, positive definiteness
- Principal Component Analysis PCA steps, explained variance, dimensionality reduction, factor extraction
- Covariance and Correlation Matrices Covariance matrix, correlation matrix, positive semi-definiteness
- Solving Linear Systems and the Matrix Inverse Solving Ax = b, LU/QR decomposition, least squares